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Answer:
0.1739 = 17.39% probability that the cab actually was blue
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Witness asserts the cab is blue.
Event B: The cab is blue.
Probability of a witness assessing that a cab is blue.
20% of 95%(yellow cab, witness assesses it is blue).
80% of 5%(blue cab, witness assesses it is blue). So
Probability of being blue and the witness assessing that it is blue.
80% of 5%. So
What is the probability that the cab actually was blue?
0.1739 = 17.39% probability that the cab actually was blue