Financial Risk Manager Part 1
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A company insures red and black cars, male and female drivers and writes policies in 2 territories ((A) and (B)). There are 300 male drivers and 200 female drivers in total. There are 150 males who drive red cars and 100 females who drive red cars. 100 male and 100 female drivers live in territory (A) and 50 of each, males and females, drive red cars in territory (A). How many drivers are either female or live in territory (B)?
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Community
NNikitesh
A
200
B
300
C
350
D
400
Explanation:
Using the principle of inclusion-exclusion: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
We need: P(female or living in territory B) = P(Female) + P(Living in territory B) - P(female and living in territory B)
Given:
- Total drivers = 300 male + 200 female = 500
- Female drivers = 200
- Drivers in territory B = Total drivers - drivers in territory A = 500 - (100 male + 100 female) = 500 - 200 = 300
- Female drivers in territory B = Total female drivers - female drivers in territory A = 200 - 100 = 100
Calculation: P(female or living in territory B) = (200/500) + (300/500) - (100/500) = 400/500
Number of drivers = (400/500) × 500 = 400
Therefore, 400 drivers are either female or live in territory B.
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