The accompanying Venn diagram illustrates a sample space containing six sample points and three events, A, B,

Question:

The accompanying Venn diagram illustrates a sample space containing six sample points and three events, A, B, and C. The probabilities of the sample points are P(1) = .3, P(2) = .2, P(3) = .1, P(4) = .1, P(5) = .1, and P(6) = .2.
a. Find P(Aˆ©B), P(Bˆ©C), P(AˆªC), P(AˆªBˆªC), P(Bc), P(Acˆ©B), P(B|C), and P(B|A).
b. Are A and B independent? Mutually exclusive? Why?
c. Are B and C independent? Mutually exclusive? Why?