We are given three coins The first coin has a head on each f

We are given three coins. The first coin has a head on each face, the second has a tail on each face, the third has one head and one tail. A coin is chosen at random and tossed and comes up heads. What is the probability that the other side of the coin is a tail.

Solution

Let H obtaining heads, A picking a two-headed coin, B picking a two-tailed coin, and C picking a fair coin.

P(AH)=P(A) * P(HA) / P(H) --> Bayes Theorem

P(A) = 1/3, as we have only 1 coin among 3 which is doubled head

P(H|A) = 1, because getting a head when u are sure its a double headed coin.

P(H) = 1/2, because in total we have 3 tails and 3 tails so 1/2 chances are there.

herefore, P(A|H) = (1/3) * 1 / (1/2) = 2/3

so chances of tail on other side = 1-2/3 =1/3