Question

BAG I contains 1 white, 2 black and 3 red balls ; BAG II contains 2 white, 1 black and 1 red balls ; BAG III contains 4 white ; 3 black and 2 red balls. A bag is chosen at random and two balls are drawn from it with replacement. They happen to be one white and one red. What is the probability that they came from BAG III?

Answer 1

Let

A : Event of drawing white ball and red ball

E₁ : Event that Bag I is chosen

E₂ : Event that Bag II is chosen

E₃ : Event that Bag III is chosen

We need to find out the probability that the red and white ball are from Bag III

i.e. P(E₃|A)

P(E₁) = Probability of Bag I = 1/3

P(A|E₁) = Probability of drawing red and white ball, if Bag I is selected

Since red can be selected, then white & white can be selected then red

P(E₂) = Probability of Bag II = 1/3

P(A|E₂) = Probability of drawing red and white ball, if Bag II is selected

Since red can be selected, then white & white can be selected then red

P(E₃) = Probability of Bag III = 1/3

P(A|E₃) = Probability of drawing red and white ball, if Bag III is selected

Since red can be selected, then white & white can be selected then red