Question

There are 5 coins in a box. 3 of them are fair coins; 2 of them are unfair coins whose probability to get a head is 70%. You pick a coin at random and toss it, and get a head. Calculate the probability that you picked an unfair coin.

Answer 1

P(fair coin) = 3/5 = 0.6

P(unfair coin) = 2/5 = 0.4

P(head | fair coin) = 0.5

P(head | unfair coin) = 0.7

P(head) = P(head | fair coin) * P(fair coin) + P(head | unfair coin) * P(unfair coin)

              = 0.5 * 0.6 + 0.7 * 0.4

              = 0.58

P(unfair coin | head) = P(head | unfair coin) * P(unfair coin)

                                 = 0.7 * 0.4 / 0.58

                                 = 0.4828 (ans)