Probability of an event that is conditonial on other events

Hi. I got a problem which is related to Probabilities Theory.

Suppose that we have a system that consists of, for example, 5 parts a, b, c, d and e. And also we have these information: If a fails, the system will fail with probability of 50%. If b fails, the system will fail with probability of 40%. And If c, d and e don't fail, the system won't fail with probability of 35%, 40% and 45% respectively.

Now this is the question:

What is the probability of the system not being failed, if a and b are failed and c, d, e, aren't. Please explain the method, too.

Thank you for your help.