(a) SupposeAandBare two events such thatP(A) = 0.2,P(B) = 0.4and:P(A|B) +P(B|A) = 0.75.

DetermineP(AB).

(b) LetAandBbe two events such that:

P((AB)^c) = 0.6andP(AB) = 0.1.

LetEbe the event that eitherAorB, but not both, occurs. DetermineP(E|AB).

(c) There are three identical boxes. Box 1 contains two gold coins, Box 2 contains two silver coins, and Box 3 contains one gold coin and one silver coin. A box is selected at random and a gold coin is drawn from the selected box. What is the probability that the other coin in the box is silver?

(d) A box contains a two-headed coin and eight fair coins. One coin is drawn at random and tossedntimes. Suppose allntosses come up heads. What happens to the probability that the coin is fair asn ? Justify your answer