easy | probability |

How do you place 50 good candies and 50 rotten candies in two boxes such that if you choose a box at random and take out a candy at random, it better be good!

We need to maximize the probability of getting a good candy when selecting a random box and a random candy from it.

Placing all bad in 1 box and all good in another will give the probability of 0.5, which is not the maximum.

Place 1 good candy in one box and all the remaining (49 good and 50 rotten candies) in the second box.

Place 1 good candy in one box and all remaining (49 good and 50 rotten candies) in the second box.

This will give a probability of $(1/2) * 1 + (1/2) * (49/99) = 74.\bar{74}\%$