(a). State and prove Bayes Theorem.

(b). Two telephones A and B are in use 0.05 and 0.3 of the total time available respectively. A is old and breaks down with probability 0.2 per unit time while B is new and breaks down with probability 0.04. If a failure indicator (F) indicates that one of the telephones is out of order, find the probability that it is A.

(c). The Probability of catching a certain type of fish from sea is 0.001. What is the probability that out of 2500 fishes caught by a fishing trawler, i. None of this type was caught ii. 5 were caught iii. At least 3 were caught.