question_answer 37)

There are three coins. One is a two headed coin, another is a baised coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows head, what is the probability that it was the two headed coin? 

Answer:

Let E1, E2 and E3 are the events of selection of a two headed coin, biased coin and unbiased coin respectively.       Let A = event of getting head             and       P(A/E3) =       Required probability = P(E1/A)