Question

There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is

Answer 1

Given:

There are two boxes, one containing 39 red balls & the other containing 26 green balls ,you are allowed to move the balls b/w the boxes.

To Find:

When you choose a box random & a ball at random from the chosen box, the probability of getting a red ball is maximized , this maximum probability is?

Solution:

here, it is given that , there are two boxes , one containing 39 red balls and other one containing 26 green balls.

Also, we are allowed to move the balls.

therefore, we keep only one red balls in first box and move all the remaining balls in 2nd box.

So, 1st box contains only 1 red ball , 2nd box contains 26 green+38 red 64 balls.

Probability of choosing any box is   $\dfrac{1}{2}$ = 0.5

So, probability of taking one red ball is

$=\dfrac{1}{2}(1)+\dfrac{1}{2}(\frac{38}{64} ) \\\\=0.5+0.296875\\=0.8$

Hence, maximum probability is 0.8