Answer: 91%

## Explanation We are given: - P(Male) = 55% = 0.55 - P(Female) = 45% = 0.45 - P(Claim|Male) = 10% = 0.10 - P(Claim|Female) = 7% = 0.07 We need to find the probability that NO ONE will have a claim. ### Step 1: Calculate the overall probability of having a claim Using the law of total probability: \[P(\text{Claim}) = P(\text{Claim} \cap \text{Male}) + P(\text{Claim} \cap \text{Female})\] \[P(\text{Claim} \cap \text{Male}) = P(\text{Claim}|\text{Male}) \times P(\text{Male}) = 0.10 \times 0.55 = 0.055\] \[P(\text{Claim} \cap \text{Female}) = P(\text{Claim}|\text{Female}) \times P(\text{Female}) = 0.07 \times 0.45 = 0.0315\] \[P(\text{Claim}) = 0.055 + 0.0315 = 0.0865\] ### Step 2: Calculate the probability of NO claim Since the probability of having a claim and having no claim are complementary events: \[P(\text{No Claim}) = 1 - P(\text{Claim}) = 1 - 0.0865 = 0.9135\] ### Step 3: Convert to percentage \[0.9135 \times 100\% = 91.35\% \approx 91\%\] Therefore, the probability that NO ONE will have a claim is approximately **91%**. **Key Concepts:** - Conditional probability: \(P(A|B) = \frac{P(A \cap B)}{P(B)}\) - Law of total probability - Complementary events: \(P(A') = 1 - P(A)\)

Author: Nikitesh Somanthe