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.

1. 85% of cabs in the city are green and the remaining cabs are blue.
2. A witness identified the cab involved in the accident as blue.
3. It is known that a witness can conectly identify the cab colour only 80% of the tune.

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%

edited

+1 vote

Probability that the cab is a green cab = 0.85

Probability that the cab is a blue cab = 0.15

The witness can correctly identify the cab colour only 80% of the time

So, probability when the witness is correct means when the witness identifies blue cab = 0.8

& Probability when witness is wrong = 0.2

We know, $P(E) = \dfrac{Numbe of favorable outcomes}{Number of all possible outcomes}$

The probability that the accident was caused by a blue cab = $\dfrac{(0.15)*(0.8)}{((0.15)*(0.8)) +((0.85)*(0.2)) }$

= $\dfrac{1.2}{2.9}$

= 0.41

= 41%     option C)

by (540 points)