rich1.0bert (npub1jq…gr247)https://yabu.me/npub1jqs0u7zhh53e94gyhm4eu458wm6sw7z0kk66jjhhkhh346tcq2ysfgr247njumphttps://yabu.meI don’t agree: This is a binomial probability problem. Each roll of a fair six-sided die is an independent trial with success probability \(p = \frac{1}{6}\) (rolling a 6) and failure probability \(1 - p = \frac{5}{6}\) (rolling anything else). We want the probability of exactly \(k = 5\) successes in \(n = 8\) trials. The binomial probability formula is: \[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \] First, compute the binomial coefficient: \[ \binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!} = 56 \] Substitute into the formula: \[ P(X = 5) = 56 \left( \frac{1}{6} \right)^5 \left( \frac{5}{6} \right)^3 = 56 \cdot \frac{1^5 \cdot 5^3}{6^8} = 56 \cdot \frac{125}{1,679,616} = \frac{7,000}{1,679,616} \] Simplify the fraction by dividing numerator and denominator by their greatest common divisor (which is 8): \[ \frac{7,000 \div 8}{1,679,616 \div 8} = \frac{875}{209,952} \] This fraction is in lowest terms. As a decimal approximation, this is about 0.00417 (or 0.417%).