Probability

Three bags contain a number of red and white balls are as follows.

Bag I: 3 red balls

Bag II: 2 red balls and 1 white ball

Bag III: 3 White balls

The probability that bag $i$ will be chosen and a ball is selected from it is $\frac{i}{6}, i=1,2,3$. If a white ball is selected, what is the probablity that it came from Bag III