Question

13 yellow balls and 14 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?

a) 1.0000

b) 0.5556

c) 0.5385

d) 0.4815

e) 0.1378

f) None of the above.

Answer 1

P(2nd ball is yellow) = P(1st ball is red and 2nd ball is yellow) + P(1st ball is yellow and 2nd ball is yellow)

                                 = 14/27 * 13/26 + 13/27 * 12/26

                                 = 0.4815

P(1st ball is red | 2nd ball is yellow) = P(1st ball is red and 2nd ball is yellow) / P(2nd ball is yellow)

                                                          = (14/27 * 13/26) / 0.4815

                                                          = 0.5384

Option-C) 0.5385