Red and Blue Marbles
You have two jars, 50 red marbles and 50 blue marbles.
A jar will be picked at random, and then a marble will be picked from the jar.
Placing all the marbles in the jars, how can you maximize the chances of a red marble being picked?
What are the exact odds of getting a red marble using your scheme?
Put one red marble in one jar (A), and the remainder in the other jar (B).
If jar A is selected, you have 100% chance of selecting a red marble.
If jar B is selected, you have 49/99 chance of selecting a red marble.
With a 50% chance of selecting jar A and a 50% chance of selecting Jar B, the odds become 50% + 50%*49/99 = 74.7474% or 148/198