Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was fair coin?

Explanation

Let `E_(1)`=Event that fair coin is drawn
`E_(2)`=Event that 2 headed coin is drawn
E=Event that tossed coin get a head
`therefore P(E_(1))=1//2,P(E_(2))=1//2,P(E//E_(1))=1//2 and P(E//E_(2))=1`
Now, using Baye's theorem `P(E_(1)//E)=(P(E_(1))cdotP(E//E_(1)))/(P(E_(1))cdotP(E//E_(1))+P(E_(2))cdotP(E//E_(2)))`
`(1/2cdot1/2)/(1/2cdot1/2+1/2cdot1)=(1/4)/(1/4+1/2)=(1/4)/(3/4)=1/3`