An experiment consists of randomly selecting one of three co

An experiment consists of randomly selecting one of three coins, tossing it, and observing the outcome heads or tails. The first coin is a fair coin, the second coin is a two-headed coin, and the third coin is a biased coin such that P(H)= 0.85.

a) What is the probability the coin lands on tails?

b) Given that the coin landed on heads, what is the probability it was the fair coin?

Solution

a) P(T) = (1/3)(0.5 + 0 + 0.15) = 0.65/3 = 0.216667

b) P(fair coin) = (1/3) x 1/((1/3)(0.5 + 1 + 0.85)) = 1/2.35 = 0.425532