Answer: 91%

## Explanation This problem involves calculating the probability that no one will have a claim using conditional probability and the law of total probability. ### Given Information: - P(Male) = 55% = 0.55 - P(Female) = 45% = 0.45 - P(Claim|Male) = 10% = 0.10 - P(Claim|Female) = 7% = 0.07 ### Step 1: Calculate Probability of Claim for Each Gender Using the conditional probability formula: \[P(\text{Claim} \cap \text{Male}) = P(\text{Claim}|\text{Male}) \times P(\text{Male}) = 0.10 \times 0.55 = 0.055\] \[P(\text{Claim} \cap \text{Female}) = P(\text{Claim}|\text{Female}) \times P(\text{Female}) = 0.07 \times 0.45 = 0.0315\] ### Step 2: Calculate Total Probability of Claim Using the law of total probability: \[P(\text{Claim}) = P(\text{Claim} \cap \text{Male}) + P(\text{Claim} \cap \text{Female}) = 0.055 + 0.0315 = 0.0865\] ### Step 3: Calculate Probability of No Claim Since the probability of no claim is the complement of having a claim: \[P(\text{No Claim}) = 1 - P(\text{Claim}) = 1 - 0.0865 = 0.9135 = 91.35\%\] Rounded to the nearest whole percentage, this gives us **91%**. ### Verification: - Male no claim probability: 0.55 × (1 - 0.10) = 0.55 × 0.90 = 0.495 - Female no claim probability: 0.45 × (1 - 0.07) = 0.45 × 0.93 = 0.4185 - Total no claim probability: 0.495 + 0.4185 = 0.9135 = 91.35% Both methods confirm the answer is **91%**.

Author: Tanishq Prabhu