You are on a game show. There are 3 bins in front of you labelled 1, 2, 3, with

Question

You are on a game show. There are 3 bins in front of you labelled 1, 2, 3, with bin 1 having 1 white balls and 1 black ball, bin 2 have 3 White and 2 Black balls and bin 3 having 5 White and 2 black balls. Without you seeing, the game show host chooses one of the bins at random (so that bin 1 gets selected with probability 1/3, the same for bin 2, 3) and then selects a ball at random from the bin selected. What is the probability the ball selected by the game show host is White? Conditional on the event that the ball selected is White, what is the chance the game show host selected bin 3 was selected?

Explanation / Answer

A) P(white)=(1/3)*(1/2)+(1/3)*(3/5)+(1/3)*(5/7)=0.604762

B) P( bin3| white )= (1/3)*(5/7)/0.604762= 0.393

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