Question

There are two boxes, one containing 21 red balls and the other containing 25 green balls. you are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting ared is maximized. this maximum probability is

Answer 1

Given that total number of red balls = 21.

Given that total number of green balls = 25.

Now, It is given that we can move the balls between the boxes.

So, We keep 1 red ball in box-1 and move 20 red balls to box-2.

Now, the total number of balls in the second box = 20 + 25 = 45.

Since 2 boxes are there, we have to select a box in (1/2) ways.

Now,

The probability of getting red ball = (1/2) * 1 + (1/2) * (20/45)

= > (1/2) + (1/2) * (20/45)

= > 13/18

= > ~0.72.

Hope this helps!