A system consists of three components that operate independently. In order for the system to work, component 1 must work, and either component 2 or 3 must work. The probability that component 1 works is 3/4, that component 2 works is 2/3 and the probabilith that component 3 works is 1/2.
a) What is the probabilith that the entire system is working?
b) if the system is broken, what is the conditional probabilith that part 2 is not working?
c) If the system is broken, what is the conditional probability that part 1 is not working?