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

Answer:

1/3

Step-by-step 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:

$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{(1/2)*(1/3)}{1/2} = 1/3$