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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.
- 6n
- n6
- 6
- 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.
- 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.