You're imprisoned by a sadistic king, who's also rather eccentric. He's devised a game in which he will guess whether a ball of a given color will be retrieved when you retrieve by randomly selecting one ball from each of four opaque vases that you will fill in his view before the selection process.

There's a sufficient supply of both red and white balls. The rules are that you will put five balls in each of the four vases. You can choose how many of each of the two colors, but the king sees how many of each you use in each. You will then select one ball from each of the four vases. The king will guess Yes or No that at least one of the balls will be white. If he's right you'll stay imprisoned or worse. If he's wrong you'll go free.

What is the best strategy for maximizing your probability of gaining your freedom? That is, what allocation of colors should be made for each vase; they need not be the same for all the vases, but each must have a total of five.

(In reply to re: If I understand the problem by Steve Herman)

Wow.  Your solution is better, since you prove the optimum distribution where I just glazed over it.

Posted by Jer on 2020-10-20 08:12:43