Probabilistic Computing MCQs (Multiple-Choice Questions)

1. What is probabilistic computing?

1. A computing approach that uses only fixed arithmetic operations without uncertainty
2. A computing approach that uses probability and randomness to process information or solve problems
3. A computing approach based exclusively on mechanical switches
4. A method that stores all information on magnetic disks

Answer: B) A computing approach that uses probability and randomness to process information or solve problems

Explanation:

Probabilistic computing incorporates probability distributions, random variables, or stochastic processes into computation. It is useful for modeling uncertainty, sampling possible outcomes, and solving problems where exact deterministic methods may be expensive or unsuitable.

2. What is a probability?

1. A numerical measure of how likely an event is to occur
2. A measure that can only represent negative values
3. The physical size of a computing device
4. The number of instructions in a program

Answer: A) A numerical measure of how likely an event is to occur

Explanation:

Probability measures the likelihood of an event and ranges from 0 to 1. A probability of 0 indicates an impossible event under the model, while a probability of 1 indicates a certain event.

3. Which statement describes a deterministic computation?

1. It always selects its output by sampling a probability distribution
2. Its output is necessarily different every time it runs
3. It produces the same output for the same input and fixed computational conditions
4. It cannot perform arithmetic operations

Answer: C) It produces the same output for the same input and fixed computational conditions

Explanation:

A deterministic computation follows fixed rules, so the same input and computational state produce the same output. A probabilistic computation may instead sample among multiple possible outcomes, although it can still produce repeatable statistical behavior.

4. What is a random variable?

1. A variable whose value is always zero
2. A variable that can store only text
3. A variable that must have a fixed value before an experiment
4. A variable that assigns numerical values to outcomes of a random process

Answer: D) A variable that assigns numerical values to outcomes of a random process

Explanation:

A random variable maps outcomes of a random experiment to numerical values. It can be discrete, such as the result of rolling a die, or continuous, such as a measured waiting time.

5. What does a probability distribution describe?

1. The number of processors installed in a computer
2. The probabilities or probability densities associated with possible values of a random variable
3. The physical layout of a computer network
4. The sequence of instructions in every deterministic program

Answer: B) The probabilities or probability densities associated with possible values of a random variable

Explanation:

A probability distribution describes how probability is assigned across possible values of a random variable. Discrete distributions assign probabilities to individual values, while continuous distributions use probability density functions to describe probabilities over intervals.

6. What is a stochastic process?

1. A collection of random variables indexed by time, space, or another parameter
2. A fixed list of computer instructions that never changes
3. A method for storing data without any variation
4. A system that cannot be modeled mathematically

Answer: A) A collection of random variables indexed by time, space, or another parameter

Explanation:

A stochastic process models the evolution of random quantities over time or another index. Examples include random walks, queueing systems, and Markov processes. Such models are useful when system behavior includes uncertainty or random variation.

7. Which probability distribution is commonly used to model the number of successes in a fixed number of independent trials with the same success probability?

1. Normal distribution
2. Exponential distribution
3. Binomial distribution
4. Uniform distribution over all real numbers

Answer: C) Binomial distribution

Explanation:

The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It is frequently used in statistical modeling and probabilistic algorithms.

8. What is the expected value of a random variable?

1. The largest value it can possibly take
2. The value that must occur in every experiment
3. The difference between the largest and smallest values
4. The probability-weighted average of its possible values, when the expectation exists

Answer: D) The probability-weighted average of its possible values, when the expectation exists

Explanation:

The expected value represents the long-run average implied by a probability distribution. For a discrete random variable, it is calculated by multiplying each possible value by its probability and summing the products.

9. What does variance measure in a probability distribution?

1. The average squared deviation from the expected value
2. The total number of outcomes in an experiment
3. The probability that every outcome is identical
4. The number of random variables in a model

Answer: A) The average squared deviation from the expected value

Explanation:

Variance measures the spread of a random variable around its expected value. A larger variance generally indicates greater dispersion, while a variance of zero means the variable is constant with probability 1.

10. Which distribution is often used to model the number of events occurring within a fixed interval when events occur at a constant average rate under suitable independence assumptions?

1. Uniform distribution
2. Poisson distribution
3. Bernoulli distribution only
4. Normal distribution exclusively

Answer: B) Poisson distribution

Explanation:

The Poisson distribution models event counts over a fixed interval under assumptions such as a constant event rate and independent occurrences. It is used in applications such as request counts, arrival modeling, and reliability analysis.

11. What is a Bernoulli random variable?

1. A variable that can take any real value with equal probability
2. A variable that always takes a value greater than 100
3. A variable with two possible outcomes, commonly represented as 0 and 1
4. A variable that cannot be described using probability

Answer: C) A variable with two possible outcomes, commonly represented as 0 and 1

Explanation:

A Bernoulli random variable represents a single trial with two possible outcomes. For example, it may represent failure as 0 and success as 1, with a specified probability of success.

12. What is the purpose of random sampling in probabilistic computing?

1. To guarantee that all possible outcomes are selected equally
2. To remove uncertainty from every model
3. To replace every probability with a fixed constant
4. To draw representative or model-based samples for estimation, inference, or exploration

Answer: D) To draw representative or model-based samples for estimation, inference, or exploration

Explanation:

Random sampling selects outcomes according to a specified sampling process or distribution. It can be used to estimate probabilities, approximate expectations, explore solution spaces, and perform inference in probabilistic models.

13. What is Bayesian inference?

1. A method that updates beliefs about unknown quantities using evidence and Bayes' theorem
2. A method that removes all uncertainty from a dataset
3. A technique used only for sorting arrays
4. A process that assumes all events have equal probability

Answer: A) A method that updates beliefs about unknown quantities using evidence and Bayes' theorem

Explanation:

Bayesian inference combines prior information with observed evidence to calculate a posterior distribution. It is widely used in probabilistic modeling, machine learning, diagnosis, and decision-making under uncertainty.

14. In Bayes' theorem, what does the prior probability represent?

1. The probability calculated only after observing all evidence
2. The probability assigned to a hypothesis before incorporating the current evidence
3. The number of samples collected from a model
4. The difference between two random variables

Answer: B) The probability assigned to a hypothesis before incorporating the current evidence

Explanation:

A prior probability represents the initial uncertainty about a hypothesis before the current evidence is incorporated. Bayesian updating combines the prior with the likelihood of the evidence to obtain a posterior probability.

15. What is a posterior probability?

1. A probability that is always equal to zero
2. A probability that does not depend on evidence
3. A probability distribution updated after considering observed evidence
4. A measure of computer memory capacity

Answer: C) A probability distribution updated after considering observed evidence

Explanation:

The posterior probability describes updated beliefs after evidence is taken into account. Bayes' theorem calculates it using the prior probability and the likelihood of the observed data, with normalization by the evidence probability.

16. What is the purpose of a Markov chain?

1. To guarantee that a random process never changes state
2. To store all data in a fixed sequence without transitions
3. To make every state transition equally likely in every system
4. To model transitions between states where the next state depends on the current state under the Markov property

Answer: D) To model transitions between states where the next state depends on the current state under the Markov property

Explanation:

A Markov chain models a sequence of states with transition probabilities. Its defining Markov property states that, given the present state, the future state is conditionally independent of the earlier history.

17. What is Monte Carlo simulation?

1. A method that uses repeated random sampling to estimate quantities or study system behavior
2. A technique that requires all outcomes to be known exactly in advance
3. A type of computer storage that uses magnetic tapes only
4. A deterministic sorting algorithm with no random inputs

Answer: A) A method that uses repeated random sampling to estimate quantities or study system behavior

Explanation:

Monte Carlo methods use random samples to estimate quantities such as expected values, probabilities, or numerical integrals. Their accuracy often improves as more independent samples are collected, although the required sample count depends on the estimator and the problem.

18. What is a major purpose of probabilistic modeling in machine learning?

1. To guarantee that training data contains no uncertainty
2. To represent uncertainty in data, model parameters, or predictions
3. To eliminate the need for evaluation
4. To ensure that all inputs receive the same prediction

Answer: B) To represent uncertainty in data, model parameters, or predictions

Explanation:

Probabilistic models can describe uncertainty about observations, hidden variables, model parameters, or future outcomes. This information can support risk assessment, prediction intervals, decision-making, and the identification of uncertain cases.

19. What is a probability mass function (PMF)?

1. A function that measures the physical mass of a computer
2. A function that must be negative for every outcome
3. A function that assigns probabilities to possible values of a discrete random variable
4. A function that describes only continuous random variables

Answer: C) A function that assigns probabilities to possible values of a discrete random variable

Explanation:

A probability mass function assigns a probability to each possible value of a discrete random variable. Its probabilities are nonnegative and sum to 1 across all possible values.

20. What does a probability density function (PDF) describe?

1. The exact probability of every individual real-valued point in a continuous distribution
2. The number of instructions executed by a processor
3. The size of a probability table in bytes
4. A density used to calculate probabilities over intervals for a continuous random variable

Answer: D) A density used to calculate probabilities over intervals for a continuous random variable

Explanation:

A probability density function describes a continuous distribution. Probabilities are obtained by integrating the density over an interval; for a continuous random variable, the probability at any single point is zero under the usual continuous-distribution model.

21. Which distribution is commonly used to model measurement errors and many naturally occurring quantities under suitable assumptions?

1. Normal distribution
2. Bernoulli distribution exclusively
3. Geometric distribution only
4. Discrete uniform distribution only

Answer: A) Normal distribution

Explanation:

The normal distribution is a continuous, bell-shaped distribution characterized by its mean and variance. It appears in many statistical models and can approximate the distribution of sums of independent random variables under conditions described by the central limit theorem.

22. What does conditional probability measure?

1. The probability of an event when no events are possible
2. The probability of one event given that another event is known to have occurred
3. The total number of outcomes in a dataset
4. The probability that all events must occur independently

Answer: B) The probability of one event given that another event is known to have occurred

Explanation:

Conditional probability measures the likelihood of an event under the information that another event has occurred. It is fundamental to Bayesian inference, probabilistic graphical models, and reasoning under uncertainty.

23. What does it mean for two events to be independent?

1. They must occur at exactly the same time
2. They must have the same probability
3. The occurrence of one does not change the probability of the other
4. They cannot occur together

Answer: C) The occurrence of one does not change the probability of the other

Explanation:

Two events are independent when the probability of their joint occurrence equals the product of their individual probabilities. Equivalently, when the relevant conditional probability is defined, knowing that one event occurred does not change the probability of the other.

24. What is a probabilistic graphical model?

1. A chart that only displays computer hardware prices
2. A diagram that contains no probability information
3. A type of image compression algorithm
4. A model that represents random variables and their probabilistic relationships using a graph

Answer: D) A model that represents random variables and their probabilistic relationships using a graph

Explanation:

Probabilistic graphical models use nodes to represent random variables and edges to describe relationships or conditional dependencies. Bayesian networks and Markov random fields are common examples used in inference and statistical modeling.

25. What is the purpose of a Bayesian network?

1. To represent conditional dependencies among random variables using a directed acyclic graph
2. To guarantee that every variable is independent of all others
3. To store files without any relationships between data items
4. To represent only deterministic arithmetic operations

Answer: A) To represent conditional dependencies among random variables using a directed acyclic graph

Explanation:

A Bayesian network represents a joint probability distribution through a directed acyclic graph and conditional probability distributions for its variables. It can support reasoning about uncertain events and updating beliefs when evidence becomes available.

26. What is stochastic gradient descent (SGD)?

1. A method that never updates model parameters
2. An optimization method that estimates gradients using individual examples or small batches of data
3. A probability distribution used exclusively for counting events
4. A hardware component that stores random numbers permanently

Answer: B) An optimization method that estimates gradients using individual examples or small batches of data

Explanation:

Stochastic gradient descent updates model parameters using gradient estimates computed from randomly selected examples or mini-batches. The estimates introduce variability but can reduce the computational cost of each update compared with calculating the full-dataset gradient.

27. What is the purpose of sampling from a probability distribution?

1. To make every possible outcome occur during each sample
2. To ensure that the distribution becomes deterministic
3. To generate outcomes according to the specified distribution
4. To remove the probabilities assigned to possible outcomes

Answer: C) To generate outcomes according to the specified distribution

Explanation:

Sampling generates outcomes according to a target probability distribution. Samples can be used for simulation, estimating expectations, making probabilistic predictions, and exploring possible states of a computational model.

28. What is a random number generator used for in probabilistic computing?

1. To guarantee that all algorithmic results are identical
2. To remove randomness from every model
3. To convert every probability into a fixed integer
4. To generate values used in random sampling or stochastic algorithms

Answer: D) To generate values used in random sampling or stochastic algorithms

Explanation:

Random number generators provide values used by sampling algorithms and randomized procedures. Pseudorandom generators use deterministic algorithms and an initial state, while physical random number generators derive randomness from physical processes.

29. What is a key difference between pseudorandom and truly random numbers?

1. Pseudorandom numbers are generated algorithmically, while physical random numbers can be derived from unpredictable physical processes
2. Pseudorandom numbers cannot be used in simulations
3. Physical random numbers are always equally distributed for every application
4. Pseudorandom numbers never repeat under any circumstances

Answer: A) Pseudorandom numbers are generated algorithmically, while physical random numbers can be derived from unpredictable physical processes

Explanation:

Pseudorandom number generators produce sequences using deterministic algorithms and internal states. Physical random number generators use measured physical processes. Both approaches can be useful, depending on statistical requirements, reproducibility needs, and security considerations.

30. What is importance sampling?

1. A method that assigns equal importance to every possible value without exception
2. A technique that samples from a convenient distribution and uses weights to estimate quantities under a target distribution
3. A method that eliminates the need for probability distributions
4. A technique that always produces an exact answer from one sample

Answer: B) A technique that samples from a convenient distribution and uses weights to estimate quantities under a target distribution

Explanation:

Importance sampling estimates expectations under a target distribution by drawing samples from another distribution and applying appropriate weights. It can reduce estimation variance when the sampling distribution is well chosen, but poor choices can lead to unstable estimates.

31. What is the main purpose of a Markov chain Monte Carlo (MCMC) method?

1. To sort a list without comparing its elements
2. To guarantee an exact sample from every distribution in a single step
3. To generate dependent samples from a Markov chain designed to explore a target probability distribution
4. To replace probability calculations with deterministic sorting

Answer: C) To generate dependent samples from a Markov chain designed to explore a target probability distribution

Explanation:

MCMC methods construct a Markov chain whose stationary distribution is the target distribution under appropriate conditions. After considering convergence and sampling behavior, the generated samples can be used to estimate expectations and perform Bayesian inference.

32. What is a major challenge in probabilistic inference for complex models?

1. Probabilities cannot be represented mathematically
2. Every random variable must be independent
3. Complex models never require data
4. The number of possible states or dependencies can make exact inference computationally expensive

Answer: D) The number of possible states or dependencies can make exact inference computationally expensive

Explanation:

Complex probabilistic models may contain many interconnected variables and a large space of possible configurations. Exact inference can become computationally intractable, so approximate methods such as sampling or variational inference are often used.

33. What is variational inference?

1. An approach that approximates a difficult probability distribution using a more manageable family of distributions
2. A method that guarantees every probability distribution can be calculated exactly
3. A technique that removes all latent variables from a model
4. A process that converts probability distributions into computer hardware layouts only

Answer: A) An approach that approximates a difficult probability distribution using a more manageable family of distributions

Explanation:

Variational inference transforms an inference problem into an optimization problem. It selects a tractable approximate distribution by optimizing an objective, often related to the evidence lower bound. Its accuracy depends on the chosen approximation family and optimization procedure.

34. What does uncertainty quantification mean?

1. Removing every uncertain observation from a dataset
2. Estimating and describing the uncertainty associated with model outputs, parameters, or predictions
3. Ensuring that every prediction is correct
4. Replacing all probability values with binary integers

Answer: B) Estimating and describing the uncertainty associated with model outputs, parameters, or predictions

Explanation:

Uncertainty quantification assesses how uncertain a model's results are. It can include probability distributions, confidence or credible intervals, prediction intervals, and sensitivity analysis, depending on the model and statistical framework.

35. How can probabilistic computing support artificial intelligence?

1. By guaranteeing perfect predictions without training data
2. By preventing machine-learning models from updating their parameters
3. By representing uncertainty in predictions and supporting stochastic learning or inference
4. By eliminating the need to evaluate model performance

Answer: C) By representing uncertainty in predictions and supporting stochastic learning or inference

Explanation:

Probabilistic methods are used in machine learning for Bayesian modeling, sampling, uncertainty estimation, and stochastic optimization. They can help a system distinguish between confident predictions and cases where available evidence provides limited support.

36. What is a probabilistic bit, often called a p-bit, in probabilistic hardware research?

1. A conventional memory bit that can only remain permanently at 0
2. A storage unit that never changes its state
3. A random variable that cannot be influenced by external inputs
4. A device or circuit element designed to fluctuate between binary states with controllable probabilities

Answer: D) A device or circuit element designed to fluctuate between binary states with controllable probabilities

Explanation:

A probabilistic bit is a hardware concept in which a binary state fluctuates stochastically, with the probability of each state influenced by control signals or interactions. Networks of p-bits are being explored for probabilistic inference, optimization, and sampling applications.

37. What is a potential use of probabilistic hardware?

1. Supporting stochastic sampling or probabilistic inference through specialized physical circuits
2. Eliminating all forms of uncertainty from the physical world
3. Guaranteeing that every algorithm requires only one operation
4. Replacing all data storage with a single random bit

Answer: A) Supporting stochastic sampling or probabilistic inference through specialized physical circuits

Explanation:

Probabilistic hardware can be designed to generate stochastic states or implement probability-based operations directly in physical circuits. Whether it provides a practical advantage depends on circuit behavior, energy use, sampling quality, scalability, and the target workload.

38. What is a potential advantage of using probabilistic computing for combinatorial optimization?

1. It guarantees the global optimum in every case
2. It can explore candidate solutions using stochastic transitions or sampling
3. It removes the need to define an objective function
4. It ensures that all candidate solutions have identical quality

Answer: B) It can explore candidate solutions using stochastic transitions or sampling

Explanation:

Many combinatorial optimization problems have large search spaces. Probabilistic algorithms can explore possible solutions through random sampling, stochastic transitions, or annealing-inspired methods. These techniques may find good solutions, but they do not guarantee a global optimum in every case.

39. What is simulated annealing?

1. A method for storing random values in permanent memory
2. A process that accepts only improvements and never explores other states
3. A stochastic optimization method that can accept worse moves according to a temperature-dependent rule
4. A deterministic sorting method based on alphabetical order

Answer: C) A stochastic optimization method that can accept worse moves according to a temperature-dependent rule

Explanation:

Simulated annealing explores a solution space by making transitions between candidate solutions. At higher temperatures, it is more willing to accept certain worse moves, helping escape local optima. The acceptance behavior generally becomes more restrictive as the temperature decreases.

40. Why is reproducibility important when evaluating a probabilistic algorithm?

1. It proves that every random outcome must be identical
2. It eliminates the need for performance measurements
3. It guarantees that a stochastic algorithm will find the global optimum
4. It allows researchers to repeat experiments and compare results under controlled conditions

Answer: D) It allows researchers to repeat experiments and compare results under controlled conditions

Explanation:

Probabilistic algorithms can produce different results across runs. Recording random seeds when applicable, input data, parameters, and evaluation procedures helps make experiments reproducible and supports meaningful comparisons of average performance and variability.

41. What does entropy measure in information theory and probability?

1. The uncertainty or average information content associated with a probability distribution
2. The physical weight of a computer processor
3. The number of instructions in a program
4. The probability that every outcome must occur simultaneously

Answer: A) The uncertainty or average information content associated with a probability distribution

Explanation:

Shannon entropy measures the average information content of outcomes under a probability distribution. For a discrete distribution, it is calculated as the negative sum of each probability multiplied by its logarithm, using a chosen logarithm base.

42. What is the law of large numbers?

1. A rule stating that random events become impossible after many trials
2. A mathematical result stating that sample averages converge toward the expected value under appropriate conditions
3. A rule stating that every sample must contain all possible outcomes
4. A method for calculating probabilities without data or assumptions

Answer: B) A mathematical result stating that sample averages converge toward the expected value under appropriate conditions

Explanation:

The law of large numbers states that the sample average approaches the expected value as the number of observations increases under suitable assumptions. It provides a theoretical foundation for estimating expectations through repeated sampling.

43. What is the central limit theorem commonly used to explain?

1. Why all probability distributions are exactly normal
2. Why every random variable has a mean of zero
3. Why the standardized sum or sample mean of many suitable independent random variables can approach a normal distribution
4. Why sampling is unnecessary in probabilistic computing

Answer: C) Why the standardized sum or sample mean of many suitable independent random variables can approach a normal distribution

Explanation:

The central limit theorem describes the conditions under which sums or sample means of independent random variables, after suitable standardization, approach a normal distribution. It is important in statistical estimation and uncertainty analysis.

44. Which statement correctly distinguishes probabilistic computing from quantum computing?

1. Every probabilistic computation requires quantum entanglement
2. Quantum computing cannot represent uncertainty
3. Probabilistic computing is identical to deterministic Boolean logic in every implementation
4. Probabilistic computing uses probability and randomness, while quantum computing relies on quantum states and operations, though quantum measurements can also be probabilistic

Answer: D) Probabilistic computing uses probability and randomness, while quantum computing relies on quantum states and operations, though quantum measurements can also be probabilistic

Explanation:

Probabilistic computing includes classical stochastic algorithms and specialized probabilistic hardware. Quantum computing uses quantum states and operations, such as superposition and entanglement in applicable systems. Although quantum measurements yield probabilistic outcomes, the two computing approaches are not interchangeable.

45. What is a major challenge when deploying probabilistic computing in safety-critical systems?

1. Assessing uncertainty, reliability, worst-case behavior, and the consequences of incorrect outcomes
2. Ensuring that every possible result is equally likely
3. Removing the need for system testing
4. Guaranteeing that no output can ever be wrong

Answer: A) Assessing uncertainty, reliability, worst-case behavior, and the consequences of incorrect outcomes

Explanation:

Safety-critical systems require careful evaluation of failure probabilities, uncertainty, and worst-case behavior. Probabilistic methods can support these systems, but their outputs and assumptions must be validated against the applicable reliability and safety requirements.

46. What is calibration in a probabilistic prediction model?

1. Increasing every predicted probability to 1
2. Ensuring that predicted probabilities correspond appropriately to observed event frequencies over suitable groups of predictions
3. Removing probability values from all model outputs
4. Guaranteeing that the model predicts the correct class every time

Answer: B) Ensuring that predicted probabilities correspond appropriately to observed event frequencies over suitable groups of predictions

Explanation:

A probabilistic model is calibrated when its predicted probabilities agree with observed frequencies in an appropriate statistical sense. For example, among events assigned a probability near 0.8, approximately 80% should occur over a sufficiently large and relevant evaluation set.

47. What is the purpose of a confidence interval in statistical estimation?

1. To guarantee that an individual future observation falls inside the interval
2. To state that the unknown parameter changes whenever new data is collected
3. To provide an interval-estimation procedure with a specified long-run coverage level under its assumptions
4. To replace every probability distribution with a single fixed value

Answer: C) To provide an interval-estimation procedure with a specified long-run coverage level under its assumptions

Explanation:

A confidence interval is constructed using a procedure designed to achieve a specified long-run coverage rate under stated assumptions. A 95% confidence procedure covers the true parameter in 95% of repeated samples under those conditions; this is not the same as saying that a fixed parameter has a 95% frequentist probability of lying in the particular interval after it has been calculated.

48. Which statement best describes the role of probabilistic computing in modern computing systems?

1. It has completely replaced deterministic computing in every application
2. It can only be used to generate random numbers and has no other applications
3. It guarantees that all machine-learning predictions are correct
4. It complements deterministic methods in tasks involving uncertainty, sampling, inference, and stochastic optimization

Answer: D) It complements deterministic methods in tasks involving uncertainty, sampling, inference, and stochastic optimization

Explanation:

Probabilistic computing is useful when a problem involves uncertainty or benefits from randomized exploration. In many practical systems, deterministic and probabilistic techniques are combined to balance accuracy, speed, resource use, and reliability.

49. A probabilistic algorithm estimates an event's probability by running 500 independent trials. The event occurs 125 times. What is the estimated probability of the event?

1. 0.10
2. 0.25
3. 0.40
4. 0.75

Answer: B) 0.25

Explanation:

Estimated probability = Number of successful trials ÷ Total number of trials.

Estimated probability = 125 ÷ 500 = 0.25.

Therefore, the estimated probability of the event is 0.25, or 25%.

50. A probabilistic computing system models a binary event with probability 0.7 of success and probability 0.3 of failure. If 200 independent trials are performed, what is the expected number of successful trials?

1. 60
2. 100
3. 140
4. 170

Answer: C) 140

Explanation:

For a binomial random variable, the expected number of successes is calculated as E(X) = n × p, where n is the number of independent trials and p is the probability of success on each trial.

Number of trials = 200.

Probability of success = 0.7.

Expected number of successes = 200 × 0.7 = 140.

Therefore, the expected number of successful trials is 140. This is an expected value; the actual number of successes may vary from one set of trials to another.