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 ____.

  1. Occur
  2. Not Occur
  3. Occur partially
  4. 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.

  1. Quantitatively
  2. Qualitatively
  3. Quantization
  4. 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.

  1. Certainty
  2. Uncertainty
  3. Both A and B
  4. 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) -

  1. Number of cases favorable to A / Number of possible outcomes
  2. Number of cases unfavorable to A / Number of possible outcomes
  3. Number of cases partially favorable to A / Number of possible outcomes
  4. 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 -

  1. m + n / m
  2. m + n / m
  3. m / m + n
  4. 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.


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

  1. Zero
  2. One
  3. Infinite
  4. None

Answer: B) One

Explanation:

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


7. Unfeasible events have ____ probability.

  1. Zero
  2. Infinite
  3. Variable
  4. 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)) = ____.

  1. 0
  2. 1
  3. Infinite
  4. 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?

  1. Trial and Event
  2. Random Experiment
  3. Outcome
  4. All of the above

Answer: D) All of the above

Explanation:

The following are the probability terms -

  1. Trial and Event
  2. Random Experiment
  3. Outcome

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

  1. Trial
  2. Event
  3. Outcome
  4. Sample Space

Answer: A) Trial

Explanation:

A trial is the performance of an experiment.


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

  1. Trial
  2. Event
  3. Outcome
  4. Sample space

Answer: B) Event

Explanation:

An event is the set of its outcomes.


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

  1. Trial
  2. Event
  3. Outcome
  4. 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?

  1. {HT}
  2. {HT,HH}
  3. {HT,TH,HH}
  4. {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.

  1. Known
  2. Random
  3. Unknown
  4. 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?

  1. Tossing a Coin
  2. Rolling a die
  3. Drawing a ball from a bag
  4. All of the above

Answer: D) All of the above

Explanation:

The following are examples of a random experiment -

  1. Tossing a Coin
  2. Rolling a die
  3. Drawing a ball from a bag

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16. ____ are the results of random experiments.

  1. Events
  2. Sample spaces
  3. Trials
  4. Outcomes

Answer: D) Outcomes

Explanation:

Outcomes are the results of random experiments.


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

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

Answer: C) Both A and B

Explanation:

The examples of outcomes are -

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

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

  1. Sample Page
  2. Sample Collection
  3. Sample Space
  4. 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 -

  1. S
  2. SS
  3. Sa
  4. 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. {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}.


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

  1. 6n
  2. n6
  3. 6
  4. n

Answer: A) 6n

Explanation:

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


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

  1. Once
  2. Twice
  3. Thrice
  4. 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.

  1. Sure
  2. Certain
  3. Complement
  4. 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 ____.

  1. Occur
  2. Never Occur
  3. Occur Often
  4. 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)?

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

Answer: C) Both A and B

Explanation:

The following are the impossible events -

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

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

  1. Sure
  2. Certain
  3. Both A and B
  4. 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)?

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

Answer: C) Both A and B

Explanation:

The following are the impossible events -

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

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

  1. Possible
  2. Impossible
  3. Occur
  4. 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)?

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

Answer: C) Both A and B

Explanation:

The following are the impossible events -

  1. Getting a head on a fair coin.
  2. 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 _____.

  1. Likely
  2. Equal
  3. Equally Likely
  4. 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.


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

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

  1. Mutually Exclusive Events
  2. Disjoint Events
  3. Both A and B
  4. 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.

  1. Mutually Inclusive
  2. Mutually Exclusive
  3. Joint event
  4. 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.

  1. Independent
  2. Exhaustive
  3. Equally Likely
  4. 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.

  1. Unequal
  2. Equally Likely
  3. Exaustive
  4. 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 -

  1. P (A ∩ B) = P (A) + P (B)
  2. P (A ∩ B) = P (A) / P (B)
  3. P (A ∩ B) = P (A) - P (B)
  4. 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 _____.

  1. Independent
  2. Dependent
  3. Equally Likely
  4. 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 -

  1. P(A ∪ B)=P(A) + P(B)
  2. P(A ∪ B)=P(A) P(B)
  3. P(A ∪ B)=P(A) / P(B)
  4. 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 -

  1. P(A ∪ B) = P(A) - P(B) - P (A ∩ B)
  2. P(A ∪ B) = P(A) + P(B) + P (A ∩ B)
  3. P(A ∪ B) = P(A) + P(B) - P (A ∩ B)
  4. 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 ____.

  1. Dependent events
  2. Independent events
  3. Like events
  4. 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.

  1. Dependent
  2. Independent
  3. Distributive
  4. 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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