Suppose that your friend has 3 coins, 2 loaded and one fair. Coin A comes up heads 70% of the time, coin B is fair, and coin C comes up tails 70% of the time. Your friend pulls a coin at random out of his pocket and offers you a bet where he gets $1 if the heads side appears. You are a bit uncomfortable with this and insist on testing the coin. Without knowing any more, you assess the probability of getting any one of the coins as 1/3.

Your friend lets you test the coin by flipping it once, and it comes up heads. Given this new information, what probability do you assign each coin? Round your answer off to the nearest thousandth.

1) C 0.167

2) B 0.400

3) C 0.200

4) A 0.527