Question

Bag A contains 2 white, 1 black and 3 red balls, Bag B contains 3 white, 2 black and 4 red balls and Bag C contains 4 white, 3 black and 2 red balls. One Bag is chosen at random and 2 balls are drawn at random from that Bag. If the randomly drawn balls happen to be red and black, what is the probability that both balls come from Bag B?

Answer 1

Let E₁, E₂ and E₃ the following events 

E₁ = Bag A chosen; E₂ = Bag B chosen; E₃ = Bag C chosen.

P(E₁) = P(E₂) = P(E₃) = 1/3

Now, the probability of drawing a red and a black ball from bag A is,