We are given four coins one has heads in both faces the seco

We are given four coins: one has heads in both faces, the second has tails in both faces, and the third and the fourth have a head in one face and a tail in the other. We choose a coin at random, toss it, and the result is a head. What is the probability that the opposite face is tail? In other words, conditioned on you observe a head, what is the probability you pick the coin which the two sides are different?

Solution

one coin picked from total= 4c1 and tossed once =>2^1

i.e denominator= 4c1*2= 8

result is head with different sides=> 2c1=2

probability= 2/8=1/4