Question

The dastardly Statistician Slayer known as Sivad Rosseforp captures you but offers you a chance to escape by playing a game. He gives you 75 red marbles, 75 white marbles, and 2 empty bowls. "Divide these 150 marbles into these 2 bowls,” he says. “You can divide them any way you like as long as you use all the marbles. Then, I will blindfold you and mix the bowls. You then can choose one bowl and remove ONE marble from it. If the marble is white you may escape, but if the marble is red, you must walk up to Chuck Norris and tell him that Bruce Lee is stronger.” How do you divide the marbles up so that you have the greatest probability of choosing a white marble? Explain your logic fully for credit

Answer 1

In this problem, we need to divide the 150 marbles in the 2 bowls, such that when a marble is randomly picked from one of the random bowl chosen then the probability of getting a white marble is maximized.

We know here that:
P(bowl 1) = P(bowl 2) = 0.5.

We maximize the probability here by having a 100% probability of getting a white bowl from one of the bowl at least. This can be done by simply putting 1 white marble in 1 of the bowl, and keeping rest of the 149 marbles in the other bowl. The probability of getting a white marble in that case randomly is computed then as:

= 0.5*1 + 0.5*(74/149)

= 0.7483

Therefore 0.7483 is the highest probability of getting a white marble in this case.