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

Answer

N/a

Explanation

Let `E_(1)=` event of selecting first coin,
`E_(2)=` event of selecting second coin,
`E_(3)=` event of selecting third coin,
and `E=` event of getting head on coin.
`:.P(E_(1))=P(E_(2))=P(E_(3))=1/3`
`P(E//E_(1))=1,`
`P(E//E_(2))=75/100=3/4,P(E//E_(3))=1/2`
`:.` Required probability
`P(E_(1)//E)=(P(E_(1)).P(E//E_(1)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//.E_(2))+P(E_(3)).P(E//E_(3)))`
`=(1/3xx1)/(1/3xx1+1/3xx3/4+1/3xx1/2)`
`=(1/3)/((4+3+2)/12)=1/3xx12/9=4/9`