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A fair six-faced die is thrown three times. The probability that the product of all three outcomes is a prime number equals n/216. Find n.
- 1
- 2
- 3
- 9
Correct answer: 9
Solution
The product is prime only when two dice show 1 and one die shows a prime (2, 3, or 5). The number of favourable outcomes is 3 (positions for the prime) * 3 (choices of prime) = 9. Total outcomes = 216, so probability = 9/216 and n = 9.
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