Probability theory, Mcqs

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1. What is the probability of rolling a 3 on a fair six-sided die?
A. 1/6
B. 1/3
C. 1/2
D. 1/4
Answer: A

2. If two events A and B are mutually exclusive, what is P(A ∩ B)?
A. P(A) + P(B)
B. P(A) × P(B)
C. 0
D. 1
Answer: C

3. What is the sum of probabilities of all possible outcomes in a sample space?
A. 0
B. 0.5
C. 1
D. 2
Answer: C

4. If P(A) = 0.3 and P(B) = 0.4, and A and B are independent events, what is P(A ∩ B)?
A. 0.12
B. 0.7
C. 0.1
D. 0.24
Answer: D

5. If an event is certain to happen, what is its probability?
A. 0
B. 0.5
C. 1
D. 2
Answer: C

6. What is the probability of drawing an ace from a standard deck of 52 cards?
A. 1/13
B. 1/26
C. 1/52
D. 1/4
Answer: A

7. If events A and B are independent, what is P(A ∪ B)?
A. P(A) + P(B)
B. P(A) × P(B)
C. P(A) + P(B) – P(A ∩ B)
D. P(A) + P(B) + P(A ∩ B)
Answer: C

8. What is the expected value of a fair six-sided die roll?
A. 3
B. 3.5
C. 4
D. 4.5
Answer: B

9. If the probability of an event is 0.75, what is the probability of its complement?
A. 0.25
B. 0.5
C. 0.75
D. 1.25
Answer: A

10. In a probability distribution, what must the sum of all probabilities equal?
A. 0
B. 0.5
C. 1
D. 2
Answer: C

11. If P(A | B) = 0.6 and P(B) = 0.5, what is P(A ∩ B)?
A. 0.1
B. 0.2
C. 0.3
D. 0.5
Answer: C

12. If you flip a fair coin three times, what is the probability of getting exactly two heads?
A. 1/2
B. 1/4
C. 3/8
D. 1/8
Answer: C

13. What is the probability of drawing a red card from a standard deck of 52 cards?
A. 1/4
B. 1/2
C. 1/3
D. 1/6
Answer: B

14. If two events A and B are mutually exclusive, what is P(A ∪ B)?
A. P(A) + P(B)
B. P(A) × P(B)
C. P(A) + P(B) – P(A ∩ B)
D. P(A ∪ B) = 1
Answer: A

15. What is the probability of rolling a total of 7 with two fair six-sided dice?
A. 1/6
B. 1/8
C. 1/12
D. 1/36
Answer: A

16. If P(A) = 0.4 and P(B | A) = 0.5, what is P(A ∩ B)?
A. 0.2
B. 0.4
C. 0.5
D. 0.6
Answer: A

17. What is the probability of drawing a king or a queen from a standard deck of 52 cards?
A. 1/13
B. 1/26
C. 2/13
D. 1/52
Answer: C

18. What is the expected value of a random variable X with P(X = 1) = 0.2, P(X = 2) = 0.3, and P(X = 3) = 0.5?
A. 1.5
B. 2
C. 2.3
D. 2.5
Answer: C

19. If you draw two cards from a deck without replacement, what is the probability that both cards are aces?
A. 1/221
B. 1/132
C. 1/169
D. 1/5525
Answer: B

20. If P(A ∪ B) = 0.8, P(A) = 0.5, and P(B) = 0.4, what is P(A ∩ B)?
A. 0.3
B. 0.2
C. 0.1
D. 0.5
Answer: B

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