Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 6 11 , then n is equal to _____

Step-by-step solution

Let E 1 event denotes the selection for 1 st bag and E 2 event denotes the selection for 2 nd bag Given P E 1 = 1 2 , P E 2 = 1 2 Let the event A = selected balls are 1 red & 1 black P A E 1 = C 1 3 × C 1 1 C 2 6 = 1 5 P A E 2 = C 1 3 × C 1 2 n + 5 C 2 = 12 n + 5 n + 4 P E 1   A = P E 1 × P A E 1 P E 1 × P A E 1 + P E 2 × P A E 2 ⇒ 1 2 × 1 5 1 2 × 1 5 + 6 n + 5 n + 4 = 6 11 ⇒ n = 4