Financial Risk Manager Part 1

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: $P(A') = 1 - P(A)$