Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
Given the following chart describing the claims of an auto insurer during a policy period and P (M|C) = .25. How many male drivers does this company insure?
| Male (M) | Female (F) | |
|---|---|---|
| Claim (C) | ? | 300 |
| No Claim (X) | 400 | 600 |
Other
Community
NNikitesh
A
200
B
400
C
500
D
600
Explanation:
Explanation:
We are given:
- P(M|C) = 0.25 (probability that a driver is male given that they made a claim)
- From the table:
- Female with claim: 300
- Male with no claim: 400
- Female with no claim: 600
- Male with claim: ? (let's call this x)
Step 1: Set up the conditional probability formula
P(M|C) = P(M ∩ C) / P(C) = x / (x + 300) = 0.25
Step 2: Solve for x
x / (x + 300) = 0.25 x = 0.25(x + 300) x = 0.25x + 75 x - 0.25x = 75 0.75x = 75 x = 100
Step 3: Calculate total male drivers
Total male drivers = Male with claim + Male with no claim Total male drivers = x + 400 = 100 + 400 = 500
Verification:
- Total claims = 100 + 300 = 400
- P(M|C) = 100/400 = 0.25 ✓
- Total male drivers = 500 ✓
Therefore, the company insures 500 male drivers.
Comments
Loading comments...