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 head what is the probability that it is was the two headed coin

Answer

`=(1xx(1)/(3))/(1xx(1)/(3)+(3)/(4)xx(1)/(3)+(1)/(2)xx(1)/(3))=(1)/(1+(3)/(4)+(1)/(2))=(1)/((4+3+2)/(4))=(4)/(9)`