System Functioning
A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of them must function properly if the system is to function properly. The probabilities of failures for the components 1 and 2 during one period of operation are 0.20 and 0.03, respectively. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. The component failures are independent.
Required:
1. What is the event corresponding to the above system failing during one period of operation?
2. What is the event corresponding to the above system functioning properly during one period of operation?
3. What is the probability that the system functions properly during one period of operation closest to:
4. The probability that the system fails during one period of operation is closest to: