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?

For such a small number of options its easy to count them 
The possible outcomes are:
heads or heads using the double head coin
tails or tails using the double tail coin
heads or tails using the fair coin
All these outcomes are equally likely.  How many of these are heads and of those how many use the double headed coin?

    $$Answer =  \frac{2}{3}$$

