Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2 N < N ! is m n where m and n are coprime, then 4 m - 3 n is equal to

Step-by-step solution

Given that, 2 N < N ! N is the sum of numbers of two dice. ⇒ 2 ≤ N ≤ 12 Let us check the given condition 2 N < N ! N = 1 (not possible) → 0 N = 2 (not possible) → 1 N = 3 (not possible) → 2 N = 4 (possible) We need to find the probability for N ≥ 4 . ⇒ P N ≥ 4 = 1 - P N = 2 - P N = 3 = 1 - 1 36 - 2 36 = 11 12 = m n Now let us find 4 m - 3 n . = 4 × 11 - 3 × 12 = 8 . Hence, the required answer is 8 .