Question

We have two coins: the first one is fair and the second one two-headed. We pick one of the coinsat random, we toss it twice and heads shows both times. Find the probability that the coin chosen is fair.

Answer 1

Pr(coin chosen is fair) = 1/8.

Explanation:

How many coins are there for selection? We have two (2) coins.

The probability of selecting any of the coin for toss is:

Pr(any of the coin) = 1/2

For the fair coin:

Pr(HH) = 1/4

For the bias coin:

Pr(HH) = 1

Therefore, the probability that the coin toss is fair, when heads shows both time is:

Pr(fair coin|HH) = Pr(fair) * Pr(HH) = (1/2)* (1/4) = 1/8.