Help needed with Probability assignment, please see attached, thank you.

Problem 4. To reduce theft, a company proposes to screen the workers with a liedetector test that has been proved correct 90% of the time (for guilty subjects, and also for innocent subjects). The company will re all the workers who fail the test. Suppose that 5% of workers steal from time to time. (a) If a worker is red, what is the conditional probability he is innocent? (b) If a worker is not red, what is the conditional probability he is guilty