Suppose that a desktop computer system consists of a monitor, a mouse, a keyboard, the computer processor itself, and storage devices such as a disk drive. Most computer system problems due to manufacturing defects occur soon in the system’s lifetime. Purchasers of new computer systems are advised to turn their computers on as soon as they are purchased and then to let them run for a few hours to see if any problems crop up. Let
A=Event that a newly purchased monitor operates properly.
B=Event that a newly purchased mouse operates properly.
C=Event that a newly purchased disk drive operates properly.
D=Event that a newly purchased computer processor operates properly.
Suppose that the four events are independent, with
P(A)=P(B)=0.98, P(C)=0.97, P(D)=0.99
Find the following probabilities:
All 4 components are working properly.
All components are working properly except for the monitor.
The monitor or the processor operates properly.
SHOW ALL YOUR WORK and Round your answers to nearest four decimal places.