Question 77

Mathematics Probability Hard

If three thrown of three dice, the probability of throwing triplets not more than twice is

(A) \(1-\frac{1}{{6}^2}\)
(B) \(1-\frac{1}{{6}^3}\)
(C) \(1-\frac{1}{{36}^2}\)
(D) \(1-\frac{1}{{36}^3}\)
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The probability of throwing a triplet is: \[ \left( \frac{1}{6} \right)^3 \times 6 = \frac{1}{36} \] The probability that a triplet is thrown in all three throws is: \[ \frac{1}{36} \times \frac{1}{36} \times \frac{1}{36} = \left( \frac{1}{36} \right)^3 \] The probability that a triplet is not thrown more than twice is: \[ 1 - \left( \frac{1}{36} \right)^3 \]

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