Question

Someone witnesses a crime involving a taxi. The witness tells the police that the taxi was blue. The police know that 77% of witnesses are correct and also that 25% of all of the taxis that could have been involved are blue while the rest are green. What is the probability that the taxi was in fact blue? Write your answer out to two decimal places.

Answer 1

Number of cases where witness reports blue taxi and it is true = 77% of 25 = 19.25

 

Number of cases where witness reports blue taxi and it is false = 23% of 75 = 17.25

 

Probability that witness is speaking true is = 19.25 / (19.25 + 17.25)

                                                                            = 52.74%

 

Probability that witness is speaking true is 52.74%.