CUET · MATHS · PYQ PAPER 2025

If two dice are rolled 12 times and getting a total greater than 4 is considered as a success, then which of the following statements are correct?
(A) The probability of getting a total greater than 4 in a single throw of the pair of dice is \(5 / 6\).
(B) Mean = 10
(C) Variance \(=3 / 5\)
(D) The probability of getting a total less than or equal to 4 in a single throw is \(1 / 6\).
Choose the correct answer from the options given below :

A (A), (B) and (D) only
B (A) and (D) only
C (A), (B), (C) and (D)
D (B) and (C) only

Verified Solution

Answer & Solution

Correct Answer

(A) (A), (B) and (D) only

Step-by-step Solution

Detailed explanation

Total outcomes for total \(\le 4\): \((1,1), (1,2), (2,1), (1,3), (2,2), (3,1)\) → 6. Total possible outcomes: \(36\). \(q = P(\text{total} \le 4) = 6/36 = 1/6\). \(p = P(\text{total} > 4) = 1 - 1/6 = 5/6\). \(\text{Mean} = np = 12 \times (5/6) = 10\).…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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