Question

A box contains three two-sided coins of the same size and weight. Coin A is a standard

unbiased coin, while Coin B has two heads. Coin C is biased so that a tail is twice as likely to

occur as the head. A coin is randomly selected from the box, tossed and landed on "heads"

What is the probability that it is Coin C?

Answer 1

$$P(A)=P(B)=P(C)=\dfrac{1}{3}$$

$$P(H|A)=\dfrac{1}{2}, P(H|B)=1, P(H|C)=\dfrac{1}{3}$$

$$P(C|H)=$$

$$=\dfrac{P(C)P(H|C)}{P(A)P(H|A)+P(B)P(H|B)+P(C)P(H|C)}$$

$$=\dfrac{\dfrac{1}{3}(\dfrac{1}{3})}{\dfrac{1}{3}(\dfrac{1}{2})+\dfrac{1}{3}(1)+\dfrac{1}{3}(\dfrac{1}{3})}=\dfrac{2}{11}$$