Answer: 0.07

## Explanation This is a binomial probability problem where: - **n = 9** (number of trials/individuals) - **p = 0.6** (probability of survival) - **q = 0.4** (probability of not surviving) - **X** = number of survivors We need to find **P(X ≥ 8)**, which means at least 8 survivors out of 9. ### Step 1: Break down the probability P(X ≥ 8) = P(X = 8) + P(X = 9) ### Step 2: Calculate P(X = 8) Using the binomial formula: $$P(X = 8) = \binom{9}{8} \cdot (0.6)^8 \cdot (0.4)^1$$ $$P(X = 8) = 9 \cdot (0.6)^8 \cdot (0.4)$$ ### Step 3: Calculate P(X = 9) $$P(X = 9) = \binom{9}{9} \cdot (0.6)^9 \cdot (0.4)^0$$ $$P(X = 9) = 1 \cdot (0.6)^9 \cdot 1$$ ### Step 4: Numerical calculation - (0.6)^8 = 0.01679616 - (0.6)^9 = 0.010077696 P(X = 8) = 9 × 0.01679616 × 0.4 = 9 × 0.006718464 = 0.060466176 P(X = 9) = 0.010077696 P(X ≥ 8) = 0.060466176 + 0.010077696 = 0.070543872 ≈ **0.071** ### Step 5: Match with options 0.071 rounds to **0.07**, which corresponds to option B. **Key points:** - This is a binomial distribution problem - The events are independent (infection of one person doesn't affect others) - The trials are identical (same survival probability for each person) - The calculation uses the binomial probability formula: $$P(X = x) = \binom{n}{x} p^x q^{n-x}$$

Author: Tanishq Prabhu