A box A contains 2 white, 3 red and 2 black balls. Another box B contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement from a randomly, selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box B is :

Step-by-step solution

Probability that box A is selected P A = 1 2 Probability that box B is selected P B = 1 2   Let E be the event that one ball is white while the other is red. ∴   P E = P A · P E / A + P B · P E / B = 1 2 2 · 3 7 C 2 + 4 · 2 9 C 2 = 1 2 6 21 + 8 36 = 1 2 2 7 + 2 9 = 16 63 Thus, P B / E = P B   P E / B P E = 1 9 16 63 = 7 16