Red and Blue Marbles Puzzle
You have two jars, 50 red marbles, 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.
Solution
Current probability is (1/2*1)+(1/2*0 )=1/2
If we decrease the number of red balls in box B1 and increase the number of red balls in box B2 then the probability of getting a red ball will be maximized.
So let us take the extreme scenario
let us take 49 red marbles from B1 to B2 then there will be 1 red ball in B1 and 99 balls in B2 out of which 49 are red and 50 of them are blue in the second jar.
If we decrease the number of red balls in box B1 and increase the number of red balls in box B2 then the probability of getting a red ball will be maximized.
So let us take the extreme scenario
let us take 49 red marbles from B1 to B2 then there will be 1 red ball in B1 and 99 balls in B2 out of which 49 are red and 50 of them are blue in the second jar.