# Statistics MCQs – Basic probability Part 1

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1. If the event of interest is A, then which of the following statements is correct?

a. the probability that A will not occur is 1 – P(A)

b. the probability that A will not occur is the probability of the complement of A

c. the probability that A will occur is zero if event A is impossible

d. the probability A will occur is one if event A is certain

e. all of the above statements are correct

Answer: E

2. Which of the following definitions is correct?

a. an activity, which results in an outcome, is called an event

b. the probability of an event is expressed in decimal form ranging from -1 to +1

c. the sample space refers to all possible outcomes of an experiment

d. the probability that an event will occur is called the experiment

e. an event is the combination of all possible outcomes

Answer: C

3. Which of the following statements is not correct?

a. if only one of the two events A and B can occur, in other words, the occurrence of one excludes the occurrence of the other event, then events A and B are mutually exclusive

b. if events A and B can occur at the same time, then A and B intersect

c. if event A does not occur, then its complement, Ā, will also not occur

d. a union of two events (eg: A or B) occurs when at least one of the two events occurs

e. If all possible outcomes of an experiment are represented in a set, the set is considered to be exhaustive

Answer: C

4. If a contingency table shows the gender and year of study of BBusSci students (ie: first year, second year, third year or fourth year) in your statistics class, which of the following statements is/are true?

a. the events “male student” and “female student” are mutually exclusive events

b. because of the fact that your stats class is a BBusSci course only, all the events are exhaustive, in other words, each student must fall into one of the classifications

c. an example for the intersection of events (eg: A and B) would be of male students who are in first year

d. an example for the union of events (eg: A or B) would be students who are female or in second year

e. all of the above statements are correct

Answer: E

5. Two events, A and B, are said to be mutually exclusive if:

a. P(A | B) = 1

b. P(B | A) = 1

c. P(A and B) = 1

d. P(A and B) = 0

e. none of the above

Answer: D

6. Two events, A and B, are said to be independent if:

a. P(A and B) = P(A).P(B)

b. P(A and B) = P(A) + P(B)

c. P(A | B) = P(B)

d. P(B | A) = P(A)

e. none of the above

Answer: A

7. Fill in the missing word in the following statement with one of the options listed below: Events are ___________ when the occurrence of one event has no effect on the probability that another event will occur.

a. mutually exclusive

b. independent

c. exhaustive

d. dependent

e. simultaneous

Answer: B

8. Fill in the missing word in the following statement with one of the options listed below: Events are ___________ when the occurrence of one event changes the probability that another event will occur.

a. mutually exclusive

b. independent

c. exhaustive

d. dependent

e. simultaneous

Answer: D

9. In the notation below, X is the random variable, c is a constant, and V refers to the variance. Which of the following laws of variance is not correct?

a. V(c) = 0

b. V(X + c) = V(X)

c. V(X + c) = V(X) + c

d. V(c X) = c^{2 }V(X)

e. all of the above are correct

Answer: C

10. You are given the following: P(A and E) = 0.17, P(Ā and E) = 0.32, P(A and Ē) = 0.17 and P(Ā and Ē) = 0.34. Which of the following statements about A and E is correct?

a. A and E are mutually exclusive and independent

b. A and E are mutually exclusive and dependent

c. A and E are not mutually exclusive but are independent

d. A and E are not mutually exclusive and are dependent

e. None of the above statements is correct

Answer: D

11. You are given the following: P(A and E) = 0.20, P(Ā and E) = 0.32, P(A and Ē) = 0.15 and P(Ā and Ē) = 0.33. Which of the following statements about A and E is correct?

a. A and E are mutually exclusive and independent

b. A and E are mutually exclusive and dependent

c. A and E are not mutually exclusive but are independent

d. A and E are not mutually exclusive and are dependent

e. None of the above statements is correct

Answer: D

12. You are given the following: P(A and E) = 0.19, P(Ā and E) = 0.38, P(A and Ē) = 0.13 and P(Ā and Ē) = 0.3. Which of the following statements about A and E is correct?

a. A and E are mutually exclusive and independent

b. A and E are mutually exclusive and dependent

c. A and E are not mutually exclusive but are independent

d. A and E are not mutually exclusive and are dependent

e. None of the above statements is correct

Answer: D

13. You are given the following: P(A and E) = 0.17, P(Ā and E) = 0.33, P(A and Ē) = 0.20 and P(Ā and Ē) = 0.3. Which of the following statements about A and E is correct?

a. A and E are mutually exclusive and independent

b. A and E are mutually exclusive and dependent

c. A and E are not mutually exclusive but are independent

d. A and E are not mutually exclusive and are dependent

e. None of the above statements is correct

Answer: D

14. You are given the following: P(A and E) = 0.16, P(Ā and E) = 0.32, P(A and Ē) = 0.12 and P(Ā and Ē) = 0.40. Which of the following statements about A and E is correct?

a. A and E are mutually exclusive and independent

b. A and E are mutually exclusive and dependent

c. A and E are not mutually exclusive but are independent

d. A and E are not mutually exclusive and are dependent

e. None of the above statements is correct

Answer: D

15. If P(A) = 0.8, P(B) = 0.3 and P(A|B) = 0.6, what is P(A and B)?

a. 0.18

b. 0.24

c. 0.03

d. 0.30

e. 0.15

Answer: A

16. If P(A) = 0.7, P(B) = 0.4 and P(A|B) = 0.6, what is P(A and B)?

a. 0.18

b. 0.24

c. 0.03

d. 0.30

e. 0.15

Answer: B

17. If P(A) = 0.8, P(B) = 0.3 and P(A|B) = 0.1, what is P(A and B)?

a. 0.18

b. 0.24

c. 0.03

d. 0.30

e. 0.15

Answer: C

18. If P(A) = 0.1, P(B) = 0.5 and P(A|B) = 0.6, what is P(A and B)?

a. 0.18

b. 0.24

c. 0.03

d. 0.30

e. 0.15

Answer: D

19. If P(A) = 0.6, P(B) = 0.3 and P(A|B) = 0.5, what is P(A and B)?

a. 0.15

b. 0.42

c. 0.27

d. 0.48

e. 0.15

Answer: A

20. If P(A) = 0.8, P(B) = 0.7 and P(A|B) = 0.6, what is P(A and B)?

a. 0.15

b. 0.42

c. 0.27

d. 0.48

e. 0.15

Answer: B