A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p . Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q . If p : q = m : n , where m and n are co-prime, then m + n is equal to

Step-by-step solution

Given, A bag contains six balls of different colours, two balls are drawn in succession with replacement, The probability that both the balls are of the same colour will be p = 6 36 Now Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q , So, probability will be q = C 1 6 × C 1 5 × C 1 4 6 4 = 120 1296 = 5 54 Now the ratio of p   &   q will be p q = 9 5 Now, on comparing with p q = m n ⇒ m + n = 14