a. 0.95 of the workers are innocent, and of those, 0.1 will be detected as guilty. This is 0.095 of the workers in total.
0.05 of the workers are guilty, and of those, 0.9 will be detected. This is 0.045 of the workers in total. Therefore, 0.095 + 0.045 = 0.14 of the workers are fired.
b. From a, we can see that the ratio of innocent to guilty is 0.095:0.045.
So, the proportion of guilty people is 0.045/0.14 ≈ 0.32
c. 0.05 of the workers were guilty, and 0.1 of those were not fired, so the total non-fired guilty people is 0.005.
0.86 of the workers were not fired, so the proportion of those that are guilty is 0.005/0.86 ≈ 0.0058
d. This question is based on opinion, so you need to answer this one yourself.