SOLUTION: An urn contains 5 white and 7 black balls. Another urn contains 3 white and 9 black balls. If one ball from the first urn is selected at random and is transferred to the second urn

Algebra ->  Probability-and-statistics -> SOLUTION: An urn contains 5 white and 7 black balls. Another urn contains 3 white and 9 black balls. If one ball from the first urn is selected at random and is transferred to the second urn      Log On


   

Question 1194849: An urn contains 5 white and 7 black balls. Another urn contains 3 white and 9 black balls. If one ball from the first urn is selected at random and is transferred to the second urn, what is the probability that the ball transferred is black given that a second ball drawn from the second urn gives a black?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


P(white from first, then black from second) = (5/12)*(9/13) = 45/156

P(black from first, then black from second) = (7/12)*(10/13) = 70/156

P(black from first, given black from second) = 70/(70+45) = 70/115 = 14/23

ANSWER: 14/23