Please explain the solutions to these questions. Question 1 a) Suppose a sample space contains 6 outcomes denoted by e1, e2, . , e6.

P (A) = 0.6, P (B) = 0.7, P (A ∪ B) = 0.5.

c) Of three events A, B, and C, suppose A and B are independent and B and C are disjoint. Their probabilities are P(A) = 0.6, P(B) = 0.2 and P(C) = 0.2. Calculate the probabilities of the following events:

(i) Both B and C occur.

(ii) At least one of A and B occurs

(iii) B does not occur.

(iv) All three events occur.