Find P(B ^C) and investigate whether events B and C are mutually exclusive

Question

P(A)= 1/3 P(A^B)= 1/12 P(C)= 1/2 P(B U C)= 5/8

A and B are independent events

Answer 1

Hi Sinat A.,

So do a Venn diagram and look for area requirements. Work the data systematically! Since p(B U C)=5/8 and P(C)=1/2, then P(B and notC)=1/8 by difference. Also, since P(A)=1/3 and P(A^B)=1/12 and they are independent, then P(B)=1/4 . Then, since P(B)=1/4 and P(B and notC) = 1/8, then P(B^C)=1/8 by difference. So they aren't mutually exclusive, if the intersection isn't null.

Right? -- Cheers, -- Mr. d.