1) The probability of A is 0.50, the probability of B is 0.45, and the probability of either (i.e. P(A[B) is 0.80. What is the probability of both A and B?

2). The probability of A is 0.30, the probability of B is 0.40, and the probability of both (i.e. P(AB) is 0.20. What is the conditional probability of A given B? Are A and B independent in a probability sense?

4. A mail-order rm considers three possible events in filling an order:
A: The wrong item is sent
B: The item is lost in transit
C: The item is damaged in transit

Assume that A is independent of both B and C and that B and C are mutually exclusive (i.e. B and C are disjoint). The individual event probabilities are P(A) = 0:02; P(B) = 0:01 and P(C) = 0:04. Find the probability that at least one of these foul-ups occurs for a randomly chosen order.
Note: think hard about how you would calculate the probability for the union of three events. That is, verify the following (a picture may help):
P(A [ B [ C) = P(A) + P(B) + P(C)