Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N - 2 , 3 N , N + 2 are in geometric progression be k 48 . Then the value of k is

Step-by-step solution

Given, Two fair dices are rolled, So total sample space will be n s = 36 Now given: N - 2 ,   3   N ,   N + 2 are in G.P. So, 3 N = N - 2 N + 2 ⇒ 3 N = N 2 - 4 ⇒     N 2 - 3 N - 4 = 0 ⇒ N - 4 N + 1 = 0 ⇒ N = 4 or N = - 1 (rejected) Now favourable cases for sum 4   ≡ 1 , 3 , 3 , 1 , 2 , 2 So, n A = 3 Hence, P A = 3 36 = 1 12 = 4 48 ⇒ k = 4