Financial Risk Manager Part 1

Explanation

We need to find the conditional probability: $P(\text{Female and Territory B} \mid \text{Black Car})$

Step 1: Organize the data

From the given information:

• Total drivers: 300 male + 200 female = 500 drivers
• Male drivers: 300 total
  • Male red car: 150
  • Male black car: 300 - 150 = 150
• Female drivers: 200 total
  • Female red car: 100
  • Female black car: 200 - 100 = 100

Territory A breakdown:

• Male drivers in A: 100
  • Male red car in A: 50
  • Male black car in A: 100 - 50 = 50
• Female drivers in A: 100
  • Female red car in A: 50
  • Female black car in A: 100 - 50 = 50

Territory B breakdown:

• Male drivers in B: 300 - 100 = 200
  • Male red car in B: 150 - 50 = 100
  • Male black car in B: 200 - 100 = 100
• Female drivers in B: 200 - 100 = 100
  • Female red car in B: 100 - 50 = 50
  • Female black car in B: 100 - 50 = 50

Step 2: Calculate the probability

$P(\text{Female and Territory B} \mid \text{Black Car}) = \frac{P(\text{Female, Territory B and Black Car})}{P(\text{Black Car})}$

Numerator: Female black car in territory B = 50

Denominator: Total black cars = Male black cars + Female black cars = 150 + 100 = 250

$P = \frac{50}{250} = 0.20 \text{ or } 20\%$

Therefore, the probability that a randomly selected black car driver is female and lives in territory B is 20%.