Question

Choose all thag apply

Which of the following are equivalent to the statement A and B are independent?

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

B. A and B cannot occur at the same time.

C. Knowing that A occurs means B cannot occur.

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

E. P(A and B)=0

F. A can happen without B happening.

G. Knowing that A occurs does not change the likelihood of B

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

Answer 1

A. Yes, equivalent.

When we say P(A)*P(B)= P(A and B), we imply that A and B are independent.

B. No, not equivalent.

This is the definition of a mutually exclusive event.

C. No, not equivalent.

This statement does not imply that the events are independent.

D. Yes, equivalent.

This means that the probability of B given A is the same as the probability of B, because B does not depend on A.

E. No, not equivalent.

This statement does not imply that the events are independent.

F. No, not equivalnet.

This does not imply independence.

G. Yes, equivalent.

H. Yes, equivalent.