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GATE 2018 EC – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. 12%
  2. 15%
  3. 41%
  4. 80%

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Show answer and explanation

Correct answer: (C) 41%

Explanation

By Bayes' theorem, $P(\text{blue}|\text{says blue})=\frac{0.15\times0.8}{0.15\times0.8+0.85\times0.2}=\frac{0.12}{0.29}=0.41$.