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:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
Total outcomes when two dice are rolled = 36
Number of outcomes with total ≤ 4: 6
Probability of total ≤ 4 = $\frac{6}{36} = \frac{1}{6}$ ✔
Probability of total > 4 = $1 - \frac{1}{6} = \frac{5}{6}$ ✔
Mean (expected value) for binomial: $\mu = n p = 12 \times \frac{5}{6} = 10$ ✔
Variance for binomial: $\sigma^2 = n p (1 - p) = 12 \times \frac{5}{6} \times \frac{1}{6} = \frac{10}{6} = \frac{5}{3}$ ❌
Correct statements: (A), (B), (D)