# Probability that we choose a two headed coin

We have a $501$ coins on the table, and assume that they have all been flipped onto that table (i.e., there is a mix of heads and tails). This also includes a two-headed coing.

Now if we pick up $1$ coin and its heads, what is the probability it is also the two-headed coin?

I've seen questions similar to this, but not the exact same. I did this out but want to hear your thoughts, before I explain how I arrived at the probability.

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What's your explanation? – Patrick Li May 17 '13 at 4:37
You pick a heads-up coin without seeing any of the other coins? – DJohnM May 17 '13 at 6:27

There are 502 "heads" on the table. Two of them are on the two-headed coin. You've picked a coin with a head, so the probability that the head you see comes from the two-headed coin is $\frac{2}{502}$ or $\frac{1}{251}$