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

P(fair coin selected and tails appear) = 1/3*1/2

P(2H coin selected and tails appear) = 1/3*0

P(biased coin selected and tails appear) = 1/3*0.15

P(a) = 1/6 + 0 + 0.05=0.2167

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A = coin landed on heads

B= it was a fair coin

P(B/A) =P(B intersection A) /P(A)

P(B intersection A) = 1/2

P(A) = 1/3 *1/2 + 1/3*1 + 1/3*0.85 = 0.7833

P(b) = 0.5/0.7833=0.638