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# Discrete Mathematics | Probability MCQs

**Discrete Mathematics | Probability MCQs**: This section contains multiple-choice questions and answers on Probability in Discrete Mathematics.

Submitted by Anushree Goswami, on November 03, 2022

**1. Probability is the likelihood that a particular event will ____.**

- Occur
- Not Occur
- Occur partially
- None of the above

**Answer:** A) Occur

**Explanation:**

Probability is the likelihood that a particular event will occur.

**2. _____ predicting the future of an event is generally possible with a certain level of accuracy.**

- Quantitatively
- Qualitatively
- Quantization
- None of the above

**Answer:** A) Quantitatively

**Explanation:**

Quantitatively predicting the future of an event is generally possible with a certain level of accuracy.

**3. Probability is used when there is _____ about the outcome of a trial.**

- Certainty
- Uncertainty
- Both A and B
- None of the above

**Answer:** B) Uncertainty

**Explanation:**

Probability is used when there is uncertainty about the outcome of a trial.

**4. In the case of an event A, the probability of its occurrence is denoted by P(A) -**

- Number of cases favorable to A / Number of possible outcomes
- Number of cases unfavorable to A / Number of possible outcomes
- Number of cases partially favorable to A / Number of possible outcomes
- Number of cases favorable to A / Number of favorable outcomes

**Answer:** A) Number of cases favorable to A / Number of possible outcomes

**Explanation:**

In the case of an event A, the probability of its occurrence is denoted by P(A) = Number of cases favorable to A / Number of possible outcomes.

**5. Event A may occur in m ways and fail in n ways, but m + n ways are equally likely to occur, so the probability of its occurrence is given by -**

- m + n / m
- m + n / m
- m / m + n
- n / m + n

**Answer:** C) m / m + n

**Explanation:**

Event A may occur in m ways and fail in n ways, but m + n ways are equally likely to occur, so the probability of its occurrence is given by m / m + n.

**6. An event that is certain to occur has a probability of ____.**

- Zero
- One
- Infinite
- None

**Answer:** B) One

**Explanation:**

An event that is certain to occur has a probability of one.

**7. Unfeasible events have ____ probability.**

- Zero
- Infinite
- Variable
- Non-real

**Answer:** A) Zero

**Explanation:**

Unfeasible events have zero probability.

**8. If P(A) is the probability of an event happening, and bar (P(A)) is the probability of it not happening, then P(A) + bar (P(A)) = ____.**

- 0
- 1
- Infinite
- None

**Answer:** B) 1

**Explanation:**

If P(A) is the probability of an event happening, and P(A) is the probability of it not happening, then P(A) + bar (P(A)) = 1.

**9. Which of the following is/are a/the probability term?**

- Trial and Event
- Random Experiment
- Outcome
- All of the above

**Answer:** D) All of the above

**Explanation:**

The following are the probability terms -

- Trial and Event
- Random Experiment
- Outcome

**10. A/an _____ is the performance of an experiment.**

- Trial
- Event
- Outcome
- Sample Space

**Answer:** A) Trial

**Explanation:**

A trial is the performance of an experiment.

**11. A/an ____ is the set of its outcomes.**

- Trial
- Event
- Outcome
- Sample space

**Answer:** B) Event

**Explanation:**

An event is the set of its outcomes.

**12. Getting a head when you toss a coin is ____.**

- Trial
- Event
- Outcome
- Sample space

**Answer:** A) Trial

**Explanation:**

Getting a head when you toss a coin is a trial.

**13. What's the event when you get a head after tossing the coin?**

- {HT}
- {HT,HH}
- {HT,TH,HH}
- {HHT}

**Answer:** C) {HT,TH,HH}

**Explanation:**

The event when you get a head after tossing the coin is {HT,TH,HH}.

**14. All potential outcomes of an experiment are known in advance in a/an ____ experiment.**

- Known
- Random
- Unknown
- Not Random

**Answer:** B) Random

**Explanation:**

All potential outcomes of an experiment are known in advance in a random experiment.

**15. Which of the following is/are an/the example(s) of a random experiment?**

- Tossing a Coin
- Rolling a die
- Drawing a ball from a bag
- All of the above

**Answer:** D) All of the above

**Explanation:**

The following are examples of a random experiment -

- Tossing a Coin
- Rolling a die
- Drawing a ball from a bag

**16. ____ are the results of random experiments.**

- Events
- Sample spaces
- Trials
- Outcomes

**Answer:** D) Outcomes

**Explanation:**

Outcomes are the results of random experiments.

**17. What is/are an/the example(s) of the outcome?**

- It is an experiment to toss a coin and get a head, which is called an outcome.
- An outcome is getting a 6 when you roll a die.
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The examples of outcomes are -

- It is an experiment to toss a coin and get a head, which is called an outcome.
- An outcome is getting a 6 when you roll a die.

**18. A _____ is a collection of all possible outcomes from an experiment.**

- Sample Page
- Sample Collection
- Sample Space
- Sample Outcome

**Answer:** C) Sample Space

**Explanation:**

A sample space is a collection of all possible outcomes from an experiment.

**19. Sample Space is denoted by -**

- S
- SS
- Sa
- Sp

**Answer:** A) S

**Explanation:**

Sample Space is denoted by S.

**20. What is a sample space, when we throw a dice?**

- {1}
- {1,2}
- {1,2,3}
- {1,2,3,4,5,6}

**Answer:** D) {1,2,3,4,5,6}

**Explanation:**

Sample space when we throw a dice is {1,2,3,4,5,6}.

**21. The total number of outcomes will be ____ if a die is rolled n times.**

- 6
^{n} - n
^{6} - 6
- n

**Answer:** A) 6^{n}

**Explanation:**

The total number of outcomes will be 6^{n} if a die is rolled n times.

**22. N dies are rolled ___ if 1 die rolls n times.**

- Once
- Twice
- Thrice
- N times

**Answer:** A) Once

**Explanation:**

N dies are rolled once if 1 die rolls n times.

**23. A ____ of an event consists of all outcomes in sample space that are not an event.**

- Sure
- Certain
- Complement
- Supplement

**Answer:** C) Complement

**Explanation:**

A complement of an event consists of all outcomes in sample space that are not an event.

**24. An impossible event is one that will ____.**

- Occur
- Never Occur
- Occur Often
- Occur Sometimes

**Answer:** B) Never Occur

**Explanation:**

An impossible event is one that will never occur.

**25. Which of the following is/are an/the impossible event(s)?**

- Getting a tail on the two-headed coin.
- Getting an 11 when a dice is thrown.
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The following are the impossible events -

- Getting a tail on the two-headed coin.
- Getting an 11 when a dice is thrown.

**26. It is called a _____ Outcome when it is an outcome that will definitely occur.**

- Sure
- Certain
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

It is called a Sure or Certain Outcome when it is an outcome that will definitely occur.

**27. Which of the following is/are an/the sure event(s)?**

- Getting a head-on two-headed coin
- Getting a 5 when a dice is thrown
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The following are the impossible events -

- Getting a head-on two-headed coin.
- Getting a 5 when a dice is thrown.

**28. ____ outcomes are outcomes that are possible to occur.**

- Possible
- Impossible
- Occur
- Non-occur

**Answer:** A) Possible

**Explanation:**

Possible outcomes are outcomes that are possible to occur.

**29. Which of the following is/are an/the possible event(s)?**

- Getting a head on a fair coin.
- Getting an odd number when rolling a die.
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

The following are the impossible events -

- Getting a head on a fair coin.
- Getting an odd number when rolling a die.

**30. If one event cannot be expected to occur in preference to another, it is said to be _____.**

- Likely
- Equal
- Equally Likely
- Unequally likely

**Answer:** C) Equally Likely

**Explanation:**

If one event cannot be expected to occur in preference to another, it is said to be equally likely.

**31. Which of the following is an equally likely event?**

- There is an equal chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6.
- There is an unequal chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6.
- There is a random chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6.
- There is no chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6.

**Answer:** A) There is an equal chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6

**Explanation:**

There is an equal chance of all six faces appearing when a die is thrown, i.e., 1, 2, 3, 4, 5, and 6.

**32. When two events cannot happen simultaneously, they are said to be ____.**

- Mutually Exclusive Events
- Disjoint Events
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

When two events cannot happen simultaneously, they are said to be mutually exclusive or disjoint events.

**33. It is _____ that a jack and a king can occur simultaneously if a card is drawn from a pack of cards.**

- Mutually Inclusive
- Mutually Exclusive
- Joint event
- Mutually Inducive

**Answer:** B) Mutually Exclusive

**Explanation:**

It is mutually exclusive that a jack and a king can occur simultaneously if a card is drawn from a pack of cards.

**34. It is called ____ events when there are all possible outcomes of an experiment.**

- Independent
- Exhaustive
- Equally Likely
- Impossible

**Answer:** B) Exhaustive

**Explanation:**

It is called exhaustive events when there are all possible outcomes of an experiment.

**35. There is an _____ relationship between events A and B when the occurrence of one event does not affect the occurrence of the other.**

- Unequal
- Equally Likely
- Exaustive
- Independent

**Answer:** D) Independent

**Explanation:**

There is an independent relationship between events A and B when the occurrence of one event does not affect the occurrence of the other.

**36. Two independent events A and B will be denoted as -**

- P (A ∩ B) = P (A) + P (B)
- P (A ∩ B) = P (A) / P (B)
- P (A ∩ B) = P (A) - P (B)
- P (A ∩ B) = P (A) P (B)

**Answer:** D) P (A ∩ B) = P (A) P (B)

**Explanation:**

Two independent events A and B will be denoted as P (A ∩ B) = P (A) P (B).

**37. Whenever one event affects the occurrence of another, it is said to be _____.**

- Independent
- Dependent
- Equally Likely
- Equally Unlikely

**Answer:** B) Dependent

**Explanation:**

Whenever one event affects the occurrence of another, it is said to be dependent.

**38. Theorem 1 states that two mutually exclusive events A and B are denoted as -**

- P(A ∪ B)=P(A) + P(B)
- P(A ∪ B)=P(A) P(B)
- P(A ∪ B)=P(A) / P(B)
- P(A ∪ B)=P(A) - P(B)

**Answer:** A) P(A ∪ B)=P(A) + P(B)

**Explanation:**

Theorem 1 states that two mutually exclusive events A and B are denoted as P(A ∪ B)=P(A) + P(B).

**39. Theorem 2 states that two non-mutual exclusive events are denoted as -**

- P(A ∪ B) = P(A) - P(B) - P (A ∩ B)
- P(A ∪ B) = P(A) + P(B) + P (A ∩ B)
- P(A ∪ B) = P(A) + P(B) - P (A ∩ B)
- P(A ∪ B) = P(A) - P(B) + P (A ∩ B)

**Answer:** C) P(A ∪ B) = P(A) + P(B) - P (A ∩ B)

**Explanation:**

Theorem 2 states that two non-mutual exclusive events are denoted as P(A ∪ B) = P(A) + P(B) - P (A ∩ B).

**40. The multiplication Theorem states that the Probability of both events occurring equals the product of their individual probabilities if A and B are ____.**

- Dependent events
- Independent events
- Like events
- Unlike events

**Answer:** B) Independent events

**Explanation:**

The multiplication Theorem states that the Probability of both events occurring equals the product of their individual probabilities if A and B are independent events.

**41. The conditional Probability Theorem states that The probability that A will occur given that B has already occurred is given by A and B if they are two _____ events.**

- Dependent
- Independent
- Distributive
- Determinant

**Answer:** A) Dependent

**Explanation:**

Conditional Probability Theorem states that The probability that A will occur given that B has already occurred is given by A and B if they are two dependent events.

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