Coin chosen is two headed coin in this probability question I have a probability question that reads:
Question: 

A box has three coins. One has two heads, another two tails and the last is a fair coin. A coin is chosen at random, and comes up head. What is the probability that the coin chosen is a two headed coin.

My attempt:
P(two heads coin| given head) = P(two heads coin * given head)/P(given head)
= 1/3/2/3 = 1/2

Not sure whether this is correct?

The answer is 2/3.
P(A∣H)=P(A) * P(H∣A) / P(H)   --> Bayes Theorem
P(A) = 1/3, because 1 out of 3 coins are 2-headed
P(H|A) = 1, because given you have the 2-headed coin, then it is for sure (100%) you will get a head
P(H) = 1/2, because there are 3 heads and 3 tails in total, so it's 50% chance to get heads
Therefore, P(A|H) = (1/3) * 1 / (1/2) = 2/3
