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. Given that a randomly selected policyholder drives a black car, what is the probability that they are female and live in territory B?

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NNikitesh

Last updated: February 2, 2026 at 10:22

20%

25%

33%

40%

Explanation:

Explanation

We need to find P(Female ∩ Territory B | Black Car) = P(Female, Territory B, Black Car) / P(Black Car)

Step 1: Organize the data

Total drivers:

Male: 300
Female: 200
Total: 500

Red car drivers:

Male red: 150
Female red: 100
Total red: 250

Black car drivers:

Male black: 300 - 150 = 150
Female black: 200 - 100 = 100
Total black: 250

Territory A:

Male in A: 100
Female in A: 100
Total in A: 200

Territory B:

Male in B: 300 - 100 = 200
Female in B: 200 - 100 = 100
Total in B: 300

Step 2: Fill the contingency table

From the given: "50 of each, males and females, drive red cars in territory A"

So:

Male red in A: 50
Female red in A: 50

Now we can complete the table:

Male drivers (300 total):

Red in A: 50
Red in B: 150 - 50 = 100
Black in A: 100 (males in A) - 50 (red in A) = 50
Black in B: 200 (males in B) - 100 (red in B) = 100

Female drivers (200 total):

Red in A: 50
Red in B: 100 - 50 = 50
Black in A: 100 (females in A) - 50 (red in A) = 50
Black in B: 100 (females in B) - 50 (red in B) = 50

Step 3: Calculate probabilities

P(Female, Territory B, Black Car) = Number of female black car drivers in territory B / Total drivers = 50 / 500 = 0.10

P(Black Car) = Total black car drivers / Total drivers = 250 / 500 = 0.50

Step 4: Conditional probability

P(Female ∩ Territory B | Black Car) = P(Female, Territory B, Black Car) / P(Black Car) = 0.10 / 0.50 = 0.20 = 20%

Verification with table:

		Territory A	Territory B	Total
Male	Red Car	50	100	150
Male	Black Car	50	100	150
Female	Red Car	50	50	100
Female	Black Car	50	50	100
Total		200	300	500

Total black cars = 150 + 100 = 250 Female black in B = 50 Probability = 50/250 = 0.20 = 20%

Therefore, the correct answer is 20% (Option A).

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