# fair and double head coin

Question : I have a fair coin and a two-headed coin. I choose one of the two coins randomly with equal probability and flip it. Given that the flip was heads, what is the probability that I flipped the two-headed coin

Probability of picking a coin is 1/2. probability of head in two headed coin is 1.

• Not quite right yet. Finish the tree showing all four leaves with probability $1/4$ for each. How many heads? Of those, how many with the unfair coin? – Ethan Bolker Apr 8 '18 at 17:15
If $DH$ stands for double-headed coin, and $H$ for Heads, you need $$p(DH|H)=\frac{p(DH\cap H)}{p(H)}$$ $$=\frac{\frac 12\times 1}{\frac 12\times 1+\frac 12\times\frac 12}$$ $$=\frac 23$$