# 3 Coin Bet

#### shangwuvn

##### New Member
A man has 3 coins as followings:
Coin 2: Tail – Tail
He selects one coin, it is a head.
He bets it is a two-head coin.
Probability in this case?

#### JohnM

##### TS Contributor
Using the classical definition of probability, it is:

probability of an event =
# ways the event of interest can occur / # possible events

...and this is a situation of conditional probability, since we are given that it is a head.

The probability that the coin is a two-headed coin is 0.5, since there are two coins that can produce a head (we are given the information that it is a head), but only 1 of the 2 is a two-headed coin.

#### shangwuvn

##### New Member
Thank you very much, Mod
However, I have another question.
Would I take the bet that it is a 2-headed coin? For sure????
Thanks a lot.

#### JohnM

##### TS Contributor
There's a 50% chance of winning, so in the long run, you'll break even.