A system is made up of to subsystems A and B connected in pa

A system is made up of to subsystems, A and B, connected in parallel. System A is made up of 5 switches connected in parallel. System B is made up of 5 switches connected in series. All switches function independently. The probability that the switch is operational is 0.7. Let P denote the Probability that the system works.

a) Find P

b) A swtich from A is operational. Find P.

c) A swtich from B is operational. Find P.

d) A switch is randomly selected (A and B are equally likely) and found to be operational. Find P

Solution

a.) P = P(A) + P(B)

P(A) = 0.7

P(B) = (0.7)^5 = 0.16807

P = 0.7 + 0.16807 = 0.86807

b.) P(A|P) = 0.7/0.86807 = 0.8064

c.) P(B|P) = 0.16807/0.86807 = 0.1936

d.) Same as P = 0.86807