A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. i. 85% of cabs in the city are green and the remaining cabs are blue. ii. A witness identified the cab involved in the accident as blue. iii. It is known that a witness can correctly identify the cab colour only 80% of the time. Which of the following options is closest to the probability that the accident was caused by a blue cab? A. 12% B. 15% C. 41% D. 80%

GATE 2018 · General Aptitude · Data Interpretation · medium

Answer: P(accident cab was blue | witness says blue) = 12/29 ≈ 41%, which is option C.

1. Compute joint probability: cab is blue AND witness says blue: P(blue and says blue) = 0.80 * 0.15 = 0.12
2. Compute joint probability: cab is green AND witness says blue: P(green and says blue) = 0.20 * 0.85 = 0.17
3. Total probability that witness says blue: P(says blue) = 0.12 + 0.17 = 0.29
4. Apply Bayes' theorem to get posterior probability: P(blue | says blue) = 0.12 / 0.29 = 12/29 ≈ 0.4138 ≈ 41%