A town has two taxi companies, Blue Taxi, whose cabs are blue in color, and Night Taxi, whose cabs are black in color. Blue Taxi has 15 cabs in its fleet, and Night Taxi has 75. Late one night, there is a hit-and-run accident involving a cab. These two taxi companies were the only ones plying their cabs that night (all 90 of their cabs were on streets at the time of the accident). A witness who saw the accident claimed that a blue colored cab was involved. A vision test for the witness under conditions similar to those on the night in question revealed that when presented repeatedly with a blue colored cab and a black colored cab, in random order, the witness could successfully identify the color of the cab 4 times out of 5.

Based on this information answer the following questions

(a)(3 pts) What is the probability that the Blue taxi company was involved in the accident that night. Please briefly show your working.

I don't know how to write the notations in word.

(.8 x .2)/(.8 x .2 + .2 x .8) = .5

It is equally likely that it was either company at fault for the accident.

(b)(3 pts) What is the probability of a Black taxi cab being involved in the accident and the witness incorrectly reporting the color of the cab involved. Please briefly show your working.