# Coins in a box: aa conditional probability problem

1. Jun 27, 2013

### Catchfire

Hello,
I've been working on some questions from Rice's Mathematical Statistics and Data Analysis and I'm not sure about my solutions.

The question I'm working on is as follows:
1.8 #59c
A box has 3 coins: 1 with two heads, 1 with 2 tails and 1 fair coin. A coin chosen randomly is flipped and comes up heads. If the coin is flipped again and comes up heads, what's the probability it's the two headed coin?

My solution:
Let A be the event the coin has two heads and let B be the event that heads is flipped twice.
P(A|B) = P(A$\cap$B) / P(B) = P(B|A)P(A) / P(B) = 1*(1/3) / P(B)

P(B) = 1/3*1 + 1/3*1/4 = 5/12

P(A|B) = 1/3 / 5/12 = 4/5

Is this correct?

2. Jun 27, 2013

### jbunniii

It looks right to me.

3. Jun 28, 2013

### Catchfire

Thanks.

Ps sorry mods, posted in wrong forum, please move to homework subforum.