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Home » The ratio of the volume of the tetrahedron to the volume of the sphere is: - Upplift

The ratio of the volume of the tetrahedron to the volume of the sphere is: - Upplift

📅 March 2, 2026 👤 scraface

Mar 02, 2026

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📌 Thus, the number of distinct sequences is $\boxed{326592}$.

📌 Question: A home-schooled student simulates genetic mutations using 3 fair 6-sided dice, each representing a gene locus. What is the probability that exactly two of the three dice show a prime number?

📌 Solution: First, identify the prime numbers between 1 and 6: $2, 3, 5$. So there are $3$ primes and $3$ non-primes ($1, 4, 6$) on each die.

📌 Probability of rolling a prime: $\frac{3}{6} = \frac{1}{2}$

📌 Probability of rolling a non-prime: $\frac{1}{2}$

📌 We want exactly two dice to show a prime. The number of ways to choose which two of the three dice show primes is $\binom{3}{2} = 3$.

📌 For each such choice:

📌 Probability for two primes: $\left(\frac{1}{2}\right)^2 = \frac{1}{4}$

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