Red Marbles Blue Marbles
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. Let us say, you put x no. of marbles in a jar and y in second jar. x+y=100. What is the value of x*y
The answer is 99.
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1 solution
To maxize your chance of picking a red marble = maximize the expected chance its red Put one red ball in one jar and the rest of the balls ( 49 red+50 blue) in the other jar. Calculate the expected chance of picking a red. 1/2 ( 1) + 1/2(49/99)= 74.74%
Any other combinations will result in less than that. So, x y=99 1=99