You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.

See Solution : Red and blue marblesLets say, we put all the red marbles in jar A and all blue marbles in jar B. Then the probability of getting a red marble is :

jar B : (1/2)*0 = 0 (selecting the jar B = 1/2, red marble from jar B = o/50)

So the maximum probability will be :

jar A : (1/2)*1 = 1/2 (selecting the jar A = 1/2, red marble from jar A = 1/1)

jar B : (1/2)*(49/99) = 0 (selecting the jar B = 1/2, red marble from jar B = 49/99)

Total probability = 74/99 (~3/4)