You have 2 jars, 50 red balls, and 50 blue balls. You need to put all the balls into the jars.

Someone is going to enter the room, randomly select a jar, and randomly select a ball from that jar.
You would like to maximize the probability of them selecting a red ball. So, for example, if you put 25 red balls in each jar and 25 blue balls in each jar, the probability of them selecting a red ball is 50%.

How can you maximize the probability of them selecting a red ball?

If you place one red ball in one jar, and the remaining balls in the second jar, the probability of selection of a red ball is maximized.

0.5 ( 1/1 + 49/99 ) = 0.7474

Any other combination will yield a lower probability.