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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.

- 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 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?

- 12%
- 15%
- 41%
- 80%

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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)**