Question

Question 2 (6 points) A system contains two components, A and B, connected in series, as shown in the diagram. Assume A and B function independently. For the system to function, both components must function. a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, b. If both A and B have probability p of failing, what must the value of pbe so c. If three components are connected in series, and each has probability p of find the probability that the system functions. that the probability that the system functions is 0.90? failing, what must the value of p be so that the probability that the system functions is 0.90?

Answer 1

a) P(A works) = 1 - P(A fails)

= 1 - 0.05

= 0.95

P(B works) = 1 - P(B works)

= 1 - 0.03

= 0.97

P(system functions) = P(both A and B functions)

= 0.95x0.97

= 0.9215

b) P(A working) = P(B working) = 1 - p

P(system functions) = P(both A and B working)

0.9 = (1 - p)²

0.9487 = 1 - p

p = 0.0513

c) P(a component working) = 1 - p

P(system functioning) = P(all three components working)

0.9 = (1 - p)³

0.9655 = 1 - p

p = 0.0345