Exactly two cab companies operate in Singapore. The Blue Company has blue cabs, and the Green Company has green cabs.?

The cab was blue or green , and a witness recognized the cab as blue or green , so 4 cases are thinkable .

Case1. The cab was a blue cab and he identified it correctly
The probability that the cab is blue is 85% , and he identifies it correctly with the probability of 80% .
So its total probability is 0.85 * 0.8 = 0.68 .

Case2. The cab was a blue cab and he identified it incorrectly
The probability that the cab is blue is 85% , and he identifies it incorrectly with the probability of 20% .
So its total probability is 0.85 * 0.2 = 0.17 .

Case3. The cab was a green cab and he identified it correctly
The probability that the cab is green is 15% , and he identifies it correctly with the probability of 80% .
So its total probability is 0.15 * 0.8 = 0.12 .

Case4. The cab was a green cab and he identified it incorrectly
The probability that the cab is green is 15% , and he identifies it incorrectly with the probability of 20% .
So its total probability is 0.15 * 0.2 = 0.03 .

But the witness Wilbur identified the car as green , so only case2 and case3 are possible .
Therefore the probability of case3 is 0.12/(0.17+0.12) = 0.4138 .

Question is incomplete... There is no actual question.