Lenny D. answered • 01/20/20

Former professor at Tufts University with decades on Wall Street

This is a kind of tricky question.. If you put all the white balls in basket one, the probability of getting a white ball from basket 1 is 1 and the probability of getting a white ball from basket 2 is zero (all the white balls are in basket 1.).. given the probability of getting basket 1 is 1/2, the probability of getting a white ball is 1/2.. If we split them equally the probability of getting a white ball in each basket is 1/2. and the probability of choosing each basket is 1/2. so the probability of getting a white ball is the prob of choosing basket one times Prob of getting a white ball in basket 1 + prob of choosing basket two times Prob of getting a white ball in basket 1. More formally let X= prob of choosing basket 1 and p1 and p2 be the probabilities of getting a white ball in basket 1 or basket 2. The Probability = Xp1 +(1-X)p1. You should be able to convince your self that if it were not a fair coin (head comes up 55% time) then you would maximize the probability of getting a white ball by putting them all into the basket which is chosen when heads appears on the coin toss.

Hope this helps

Lenny