Please help with conditional probability problem?

Over 50% of all engineers end up in management. An engineering firm needs project managers that understand the technical aspects of the product. A large firm is looking toward future needs. A look at personnel records indicates 30% of their current engineers (who are not yet in management positions) have an electrical engineering degree, 42% have a mechanical engineering degree,and 21% have a software engineering degree. 27% of all the engineers have some management training. Specifically, 11% have an electrical engineering degree and management training, 9% have a mechanical engineering degree and management training, and 2% have a software engineering degree and management training.

a)What is the probability that an engineer (any engineer) will not have had any management training?

b)What is the probability that an engineer with a mechanical engineering degree has had management training?

c)What is the probability an engineer will have some other degree or management training but not both

1 answer

a) 1 - .27 = ?

However, the ones with some degree beside management training (27%) do not add up when the engineering degrees are summed (11% + 9% + 2% = 22%). What about the other 5%?