There are three coins in a box One is a twoheaded coin anoth

There are three coins in a box. One is a two-headed coin, another is a two-tailed coin, and the third is a fair coin. When one of the three coins is selected at random and flipped, it shows head. What is the probability that it is the two-headed coin?

Solution

Answer

Let H be the event of getting heads , A be the event of selecting two - headed coin , B be the event of getting          two - tailed coin and C be the event of getting fair coin.

Then observe that the probability of obtaining a head is:

P(H) = P(A) . P(H/A) + P(B) . P(H/B) + P(C) . P(H/C)

       = ( 1/ 3) ( 2/2 ) + ( 1/3 )( 0/2 ) + ( 1/3 ) ( 2/2 )

      = ( 1/3 ) + 0 + ( 1/3 )

      = 2/3