Answer:
a) 0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular.
b) 0.3379 = 33.79% probability it actually is irregular
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.
a. What is the probability the detector will identify a random mile of roadway as irregular?
99% of 3%(it is irregular).
6% of 97%(false positive). So

0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular.
b. Given a randomly selected miles has been identified as irregular by the detector, what is the probability it actually is irregular? Give your answer to four decimal places.
Conditional probability:
Event A: Identified as irregular
Event B: It is irregular.
0.0879 = 8.79% probability the detector will identify a random mile of roadway as irregular, which means that

99% of 3% arre irregulars identified as, which means that

The desired probability is:

0.3379 = 33.79% probability it actually is irregular