The accompanying Venn diagram illustrates a sample space containing six sample points and...

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(A ∩ B),P(B ∩ C),P(A ∪ C),P(A ∪ B ∪ C), P(Bc), P(Ac ∩ 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?