Mathematics

Problem

For three events

A,\,B

and

C

the following probabilities are given:

P(A)=0.5,\;P(B)=0.4,\;P(C)=0.3,

P(A\cap B)=0.20,\;P(A\cap C)=0.15,\;P(B\cap C)=0.12,

P(A\cap B\cap C)=0.05.

Which one of the following statements is correct? a) Only

A

and

B

are independent b)

A,\,B

and

C

are pairwise independent but not mutually independent c)

A,\,B

and

C

are mutually independent d) No two of the events are independent