# Easy conditional probability question

• Apr 22nd 2011, 07:57 AM
IanCarney
Easy conditional probability question
Tia and Jerry are tossing two coins. Tia wins when both coins turn up tails. The coins are tossed but roll under a chair. Jerry looks under the chair and, seeing both coins, says, "At least one of them is tails." What is the probability that Tia wins?

The way I thought of it was:

P(Both tails | At least one tail)

= \frac{P(both tails)}{P(at least one tails)}

= \frac{\frac{1}{2}}{\frac{1}{4}}

But the answer in the book is \frac{1}{3}

Can anyone tell me where I'm going wrong/how I should be doing questions like this? Thanks!
• Apr 22nd 2011, 08:03 AM
Plato
Quote:

Originally Posted by IanCarney
Tia and Jerry are tossing two coins. Tia wins when both coins turn up tails. The coins are tossed but roll under a chair. Jerry looks under the chair and, seeing both coins, says, "At least one of them is tails." What is the probability that Tia wins?
But the answer in the book is \frac{1}{3}
Can anyone tell me where I'm going wrong/how I should be doing questions like this? Thanks!

Knowing that at least one is a tail this is the outcome space {TT, TH, HT}
She wins 1 out of 3.
• Apr 22nd 2011, 08:07 AM
IanCarney
Quote:

Originally Posted by Plato
Knowing that at least one is a tail this is the outcome space {TT, TH, HT}
She wins 1 out of 3.

Ah, I get it. Thanks a lot!