Suppose there has been a hit-and-run accident. A person was struck by a taxicab

Question

Suppose there has been a hit-and-run accident. A person was struck by a taxicab last night. There are

two cab companies in town, Blue Cab and Green Cab. The only witness, who was some distance away,

believes it was a blue vehicle he saw cause the accident. Which cab company is guilty? How much do we

know?

How would it affect your conclusion if you also knew:

Green Cab Company had 90 cabs on the street at the time of the accident, while Blue Cab

Company had only 10 cabs out.

Given the lighting and visibility at the time of the accident, a person could correctly distinguish a

blue from a green cab about 80% of the time, at the distance the witness said he was from the

accident. (One can always tell if it was a taxicab or not.)

a.

What is the probability that the witness would report seeing a blue cab?

b. What is the probability given that the witness claims he saw a blue cab, that it actually was a

blue cab?

Explanation / Answer

a)

probability that the witness would report seeing a blue cab =P(blue cab and witness saw a blue cab)+P(green cab and witness saw a blue cab)

=(10/100)*0.8+(90/100)*(1-0.8)=0.26

b)

P(blue cab|witness saw blue cab)=P(blue cab and witness saw a blue cab)/P(saw blue cab)

=(10/100)*0.8/0.26=0.3077

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