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 of the pair of dice is 1/6.

Choose the correct answer from the options given below:

When rolling two dice together, success is defined as getting a total greater than 4.

The outcomes where total ≤ 4 are:

Total of 2: (1,1) → 1 way

Total of 3: (1,2), (2,1) → 2 ways

Total of 4: (1,3), (2,2), (3,1) → 3 ways

Total ways to get ≤ 4 = 1 + 2 + 3 = 6 ways

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Total possible outcomes when rolling two dice = 6 × 6 = 36

$P(\text{total} \leq 4) = \frac{6}{36} = \frac{1}{6}$

Statement D is correct.

$P(\text{total} > 4) = 1 - \frac{1}{6} = \frac{5}{6}$

Statement A is correct.

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The experiment follows a Binomial Distribution with:

$n = 12$ (number of trials)

$p = \frac{5}{6}$ (probability of success)

$q = 1 - p = \frac{1}{6}$ (probability of failure)

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Mean = $n \times p$

Mean = $12 \times \frac{5}{6}$

Mean = $10$

Statement B is correct.

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Variance = $n \times p \times q$

Variance = $12 \times \frac{5}{6} \times \frac{1}{6}$

Variance = $12 \times \frac{5}{36}$

Variance = $\frac{60}{36} = \frac{5}{3}$

Statement C claims variance = $\frac{3}{5}$, which is incorrect since $\frac{5}{3} \neq \frac{3}{5}$.

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Statements (A), (B), and (D) are correct.