Answer: 20%

## 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).

Author: Nikitesh Somanthe