five ordinary quarters and a fake quarter with two heads are places in a hat. One quarter is selected at random and tossed twice. If the outcome is "HH", what is the probability that the fake quarter was selected?

Question

anonymous · Answer

1/6 I'd say

anonymous · Answer

Ok, You have observed HH. The probability of getting that with a fair coin is 1/4, and you have a 4/5 chance of getting that.
The probability of getting HH with your fake coin is 1 (has to happen), but you have a 1/5 chance of getting this. So there is 
1/4*4/5 + 1/5 = 2/5 chance that you get HH for a random coin in the bag.  
But you got HH, so you treat that as if it is 100%, and your answer is P(fake HH)/P(total HH)=1/5 / 2/5 = 1/2 or 0.5

anonymous · Answer

functional, how do you have a 1/5 chance of getting the fake coin if there are 6 coins in the bag?