"It is known that a witness can correctly identify the cab colour only 80% of the time."

and

"It is known that a witness can correctly identify EACH cab colour only 80% of the time." ?

Dark Mode

Lakshman Patel RJIT
asked
in Quantitative Aptitude
Feb 21, 2018
retagged
May 29, 2019
by Pooja Khatri

3,858 views
7 votes

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.

- $85\%$ of cabs in the city are green and the remaining cabs are blue.
- A witness identified the cab involved in the accident as blue.
- 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?

- $12\%$
- $15\%$
- $41\%$
- $80\%$

11 votes

Best answer

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, $\bf{P(E) = \dfrac{\text{Number of favourable outcomes}}{\text{Number of all possible outcomes}}}$

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

$\qquad= \dfrac{1.2}{2.9}$

$\qquad= 0.41$

$\qquad= 41\%$** **

**Option (C)**

0