A probability question, please help!?

There are six possible outcomes :

Head )
. . . . .) . . from the fair coin
Tail. . )


Head )
. . . . .) . . from the two-headed coin
Head )

Tail . )
. . . . .) . . from the two-tailed coin
Tail . )


Three of the outcomes show a head, and two of them come from the two-head coin. Therefore the probability that it WAS the two-head coin = 2/3.

2/3 of a chance

1/3 chance for which coin you will take out of the bag.
The fair coin has 1/2 chance of landing heads or tails.
The double headed coin has a 2/2 chance of landing heads.
And the double headed tails coin has 2/2 chance landing tails.

There is exactly 50% chance that you will flip heads, and 50 percent chance you will flip tails.
2/3 chance you will pick the double headed coins.

applying the law of total probability,

.................... fair coin ... 2 tailed 2 headed
P(heads) = 1/3 * 1/2 + 1/3*0 + 1/3 * 1 = 0.5

P(2 headed | heads] = (1/3 *1) / 0.5 = 2/3 <-----------