Bayes theorem

[Guest]

Three bags I, II and III contain 1 white, 2 black and 3 red balls; 2 white, 1 black, and 1 red balls; and 4 white, 5 black and 3 red balls, respectively. One bag is selected at random and two balls are drawn. These happen to be one white and one red. Find the probability that these balls were drawn from bag I.

[shyamjayakannan]

[tex]\displaystyle\frac{\displaystyle\frac{1\times3}{^6C_2}}{\displaystyle\frac{1\times3}{^6C_2}+\frac{2\times1}{^4C_2}+\frac{4\times3}{^{12}C_2}}=\displaystyle\frac{\displaystyle\frac{1}{15}}{\displaystyle\frac{1}{15}+\frac{1}{3}+\frac{2}{11}}=\boxed{\frac{11}{96}}[/tex]