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 i 6 , i=1,2,3 . if a white ball is selected, what is the probablity that it came from Bag III

Step-by-step solution

Let B₁, B₂, B₃ be the events of choosing Bag I, Bag II, and Bag III respectively. Let W be the event of selecting a white ball. The probabilities of choosing the bags are given by P(B₁) = 1 6 , P(B₂) = 2 6 = 1 3 , and P(B₃) = 3 6 = 1 2 . The conditional probabilities of selecting a white ball from each bag are: P(W|B₁) = 0 3 = 0 P(W|B₂) = 1 3 P(W|B₃) = 3 3 = 1 Using the law of total probability, the probability of selecting a white ball is: P(W) = P(B₁)P(W|B₁) + P(B₂)P(W|B₂) + P(B₃)P(W|B₃) P(W) = ( 1 6 0 ) + ( 2 6