Question

Consider 100 balls of which 90 are red and 10 are white. A random sample of 50 of the balls is placed in an urn, while the remaining 50 balls are placed in a second urn. One ball is sampled from the first urn. It is white. This white ball is placed in the second urn. A ball is then sampled at random from the second urn. Find the probability that the second ball sampled is white.

Answer 1

since the ball selected from first urn is white , there should be atleast one white ball in urn 1

if exactly 1 white ball goes to urn 1 , then 9 white and 41 black in urn 2 in

if exactly 2 white ball goes to urn 1 , then 8 white and 41 black in urn 2 in

.........

if exactly 10 white ball goes to urn 1 , then 0 white and 50 black in urn 2 in

after transfering 1 white from urn 1 to urn 2

number of balls in urn 2 is 51

and number of white balls is either 1 or 2 or 3 or......or 10

probability of choosing white from urn 2 is

+ +..........+