Question

Two cab companies operate in River City, the blue and the green, named according to the colors of the cabs they run. 85% of the cabs in River City are blue cabs and 15% are green cabs. a cab was involved in a hit and run accident at night. an eyewitness later identified the cab as green. the court tested the witness's ability to distinguish between blue and green cabs under nightitme visibiltiy conditions. it found the witness was able to identify each color correctly 80% of the time, but he confused it with the other color 20% of the time. What is the probability that the cab in the accident

Answer 1

really was green, as the witness claimed it was?

Answer 2

is it 80% times 15% ?

Answer 3

Hmm. so basically we need to find the probability of 'truth' right.

Since the witness claims that the was was green, he following events may have happened
---> 'A'=The cab was actually green & the witness spotted it correctly---> 0.15 times 0.80
---> 'B'=The cab was blue actually and the witness spotted it wrongly---> 0.85 times 0.20


The sum of Ps of the two cases = 0.12 + 0.17

P of favourable condition 'A' ---> 0.12

Answer 4

yes that is the absolute P for it, but you need to find the conditional probability.

Answer 5

whats that? how do you go about finding it?

Answer 6

I just provided you with the sum of the conditions. and there is that favorable condition too.
so P = (favorable probability)/(Total probability) = 0.12/(0.12+0.17) = 0.12/0.29

Answer 7

ohhhhhh. thanks dude.

Answer 8

No probs, hope you understood the concepts there.

Answer 9

i did! :)