Question

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?

Answer 1

A be the event-coin shows head
B be the event-two headed coin shows head.
C be the event-biased coin shows head.
D be the event-unbiased coin shows head.
`P(B/A)=(P(A/B)P(B))/(P(A/B)P(B)+P(A/C)P(C)+P(A/D)P(D))`(BAYES THEOREM)
All coins are equally probable
`P(B/A)=(1xx1/3)/(1xx1/3+3/4xx1/3+1/3xx1/2)=4/9`