# 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

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

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

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.

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

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

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

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

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

Explanation:

A trial is the performance of an experiment.

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

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

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

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}

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

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

16. ____ are the results of random experiments.

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

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}

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.

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

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

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

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)?

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 -

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

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.

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

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

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

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

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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