Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that are in geometric progression be . Then the value of k is
- A.16
- B.2
- C.4
- D.8
Show answer and solution
Correct option: C
Solution
For N-2, √(3N), N+2 to be in GP, the middle term squared equals the product of the outer terms:
(√(3N))² = (N-2)(N+2)
3N = N² - 4
N² - 3N - 4 = 0
(N-4)(N+1) = 0
N = 4 (since N must be positive)
Now count ways to get N=4 with two dice: (1,3), (3,1), (2,2) → 3 favorable outcomes out of 36 total.
Probability = 3/36 = 1/12 = 4/48, so k = 4.
(√(3N))² = (N-2)(N+2)
3N = N² - 4
N² - 3N - 4 = 0
(N-4)(N+1) = 0
N = 4 (since N must be positive)
Now count ways to get N=4 with two dice: (1,3), (3,1), (2,2) → 3 favorable outcomes out of 36 total.
Probability = 3/36 = 1/12 = 4/48, so k = 4.
[JEE Main 2023 · 25 Jan · Shift 2]