Urn I contains 5 red balls and 5 white balls. Urn II contains 12 white balls. A ball is selected at random from urn I and placed in urn II. Then a ball is selected at random from urn II. What is the probability that the second ball is white?

Question

anonymous · Answer

case 1. Let the ball selected from urn one is red then probability that it is red is 5/10=.5 and then this white ball is added to 2nd urn now there are all 13 white balls so probability that a ball is white taken out of 2nd urn is 1.Hence ,overall probability is .5 * 1 =.5
Case 2nd .Now let us assume that the ball was red taken out of urn 1 then the probablity of being red is 5/10 =.5 and then placed in urn 2nd.Urn 2 has now 1 red and 12 white balls and hence probability of ball taken out of urn 2 being white is 12/13 .therefore overall probability is .5*12/13.

therefore,total probability is .5 +6/13 =.9615