Mathematics

Problem

Suppose events

A

B

, and

C

satisfy

P(A \cap B \cap C)=P(A)P(B)P(C)

. Which of the following statements is necessarily true? a)

A

B

, and

C

are pairwise independent but not necessarily mutually independent. b) No conclusion about independence can be drawn without further information. c)

A

B

, and

C

are mutually independent. d)

A

and

B

are independent but

C

may depend on them.