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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 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. $80\%$

### 1 comment

What is the difference between the statements :

"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." ?

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)

What is the difference between the statements :

"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." ?
There is no difference between these two statements.