3 Coin Bet

#1
Please help me with this problem
A man has 3 coins as followings:
Coin 1: Head – Head
Coin 2: Tail – Tail
Coin 3: Head – Tail
He selects one coin, it is a head.
He bets it is a two-head coin.
Probability in this case?
Please help me,
Thank you in advance.
 

JohnM

TS Contributor
#2
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.

P(2-headed | head) = 1/2