Probability Problem

1. Jul 22, 2014

Debdut

An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. 2 balls are drawn at random from the first urn and placed in the second urn and 1 ball is drawn at random from the second urn. What is the probability that it is white?

2. Jul 22, 2014

micromass

Staff Emeritus
Please tell us why you think that.

3. Jul 22, 2014

xiavatar

4. Jul 22, 2014

Ray Vickson

I also get 59/130. Nevertheless, the OP should show his/her work.

5. Jul 22, 2014

Debdut

I don't know whether I have done it correctly or not...

There are 4 combinations of picking 2 balls from 1st urn (White → W, Black → B)

WW → P = 10/13 x 9/12 = 15/26
BB → P = 3/13 x 2/12 = 1/26
WB → P = 10/13 x 3/12 = 5/26
BW → P = 3/13 x 10/12 = 5/26

If WW was picked, then balls in 2nd urn = 5W 5B, Then probability of picking white ball = 5/10
If BB was picked, then balls in 2nd urn = 3W 7B, Then probability of picking white ball = 3/10
If WB was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10
If BW was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10

Thus total probability of picking white ball from 2nd urn = (5/10 x 15/26)+(3/10 x 1/26)+(4/10 x 5/26)+(4/10 x 5/26) = 59/130

6. Jul 23, 2014

HallsofIvy

Staff Emeritus
Yes, that is correct.