SOLUTION: Pretty stuck on this one! You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the balls in the boxes in any way you like. You th

Question 470344: Pretty stuck on this one!
You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the balls in the boxes in any way you like. You then are asked to select a box (after the boxes have been shuffled) and to pick a ball at random from that box. If the ball is red, you win a prize. How should you distribute the balls in the boxes to maximize your chances of winning? Justify your reasoning.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
You are given three white balls, one red ball, and two identical boxes. You are asked to distribute the balls in the boxes in any way you like. You then are asked to select a box (after the boxes have been shuffled) and to pick a ball at random from that box. If the ball is red, you win a prize. How should you distribute the balls in the boxes to maximize your chances of winning?
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First, you have to choose a box. So the probability of choosing the box containing the red ball is 1/2.
Now the probability of selecting a red ball out of the properly selected box is
1/n, where n is the total number of balls in that box.
So we can write the probability for selecting a red ball as:
P(red) = (1/2)(1/n)
This probability will be maximized when n = 1. In other words, when the red ball is the only ball in the box.
So the balls should be distributed with the 3 white balls in one box
and the one red ball in the other box.

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