Three are three coins in a bag. Coin 1 (call it C1) is a fair coin, coin 2 (call it C2) and coin 3 (call it C3) are both biased with coin 2 having heads on both sides and coin 3 having tails on both...

Extracted text: Three are three coins in a bag. Coin 1 (call it C1) is a fair coin, coin 2 (call it C2) and coin 3 (call it C3) are both biased with coin 2 having heads on both sides and coin 3 having tails on both sides. You randomly chose one and tossed it twice. (c) Find the probability of obtaining two heads. (d) Suppose you obtained two heads but you didn't know which coin was chosen. Which theorem can help find the conditional probability that the fair coin is chosen given two heads were obtained? (e) Find the conditional probability that the fair coin is chosen given two heads were ob- tained.