Maximize probability of White Ball — Puzzle for Interview rounds

Question :

There are two empty bowls in a room. You have 50 white balls and 50 black balls. After you place the balls in the bowls, a random ball will be picked from a random bowl. Distribute the balls (all of them) into the bowls to maximize the chance of picking a white ball.

Solution :

First, let us assume that we divided the balls into jars equally so each jar will contain 50 balls.
So the probability of selecting a white ball will be=probability of selecting the first jar*probability of white ball in the first jar + probability of selecting the second jar*probability of white ball in the second jar
=(1/2)*(0/50)+(1/2)*(50/50)=0.5
Since we have to maximize the probability so we will increase the probability of white ball in the first jar and keep the second probability same mean equal to 1
so we add 49 white balls with 50 black balls in the first jar and only one white ball in the second jar
so the probability will be now = (1/2)*(49/99)+(1/2)*(1/1)=0.747

Therefore, probability of getting white ball becomes 1/2*1 + 1/2*49/99 which is approximately 3/4.

Thanks for Reading

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