Question

Suppose you have three nickels in a jar, where the first has Heads on both sides, the second has Tails on both sides, and the third is a fair coin. You choose one coin at random and toss it. The toss results in Tails. What is the probability that you chose the fair coin?

Answer 1

1/3

Explanation:

Let A be the event that you grab the fair coin and B be the event that you toss a tail.

P(A) is the probability that you grab the fair coin, which is 1/3

P(B) is the probability that you toss a tail, which is 1/2

P(B|A) is the probability that you toss a tail, given that you grab a fair coin, which is 1/2

P(A|B) is the probability that you grab the fair coin, given that you toss a tail, which we are looking for.

Using Bayes probability theorem we have:

`P(A|B) = (P(B|A)P(A))/(P(B)) = ((1/2)*(1/3))/(1/2) = 1/3`