You have been called for jury duty in a town where there are two taxi companies, Green Cabs Inc and Blue Taxi Ltd. Blue Taxi uses cars painted blue; Green Cabs uses cars painted green. Green Cabs dominates the market with 85% of the taxis on the road.
On a misty night a taxi sideswiped another car and drove off. A witness says it was a blue cab. The witness is tested under conditions like those on the night of the accident, and 80% of the time correctly reports the color of the car that is seen (whether it is green or blue).
What do you think of the chance that the sideswiper was blue (as the witness asserts)?
Please show all steps with explanations. Thanks!
On a misty night a taxi sideswiped another car and drove off. A witness says it was a blue cab. The witness is tested under conditions like those on the night of the accident, and 80% of the time correctly reports the color of the car that is seen (whether it is green or blue).
What do you think of the chance that the sideswiper was blue (as the witness asserts)?
Please show all steps with explanations. Thanks!
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P[color blue & reported blue] = 15% * 80% = 12%
P[color green & reported blue] = 85% * 20* = 17%
P[reported blue] = sum of the above = 29%
P[color blue | reported blue] = 12/29 or 41.38% <----------
P[color green & reported blue] = 85% * 20* = 17%
P[reported blue] = sum of the above = 29%
P[color blue | reported blue] = 12/29 or 41.38% <----------