Question

There are two boxes, one containing 32 black balls and other containing 31 red balls you are allowed to move the boxes at random so that when you choose the box at random and a ball at random from the chosen box, the probability of getting the black ball is maximized. This maximum probability is

Answer 1

Move 31 balls from red ball box to other box having 31 green balls.

now one box has one red ball

and

other box is having 31 red balls and 31 green balls.

then prob of getting red ball = 1/2 (1+31/62) = 1/2 *3/2 =3/4=0.75