Question

Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two- headed coin. He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?

Answer 1

Let F shows the event that a fair coin is selected and U shows the event that unfair coin is selected. So we have

P(F) = 2/ 3 , P(U) = 1/3

Let H shows the event of getting head. Probability of getting head with fair coin is 0.5 and with unfair coin is 1. So we have

P(H | F) = 1/2 = 0.50

P(H |U) = 1

By the Baye's theorem the probability that coin is fair given that he gets head is

P(F |H) = [ P(H|F)P(F) ] / [ P(H|F)P(F) + [ P(H|U)P(U) ] = [ 0.50* (2/3) ] /[ 0.50* (2/3) + 1* (1/3)] = 0.50

Answer: 0.50