Example: A system consists of three components connected as shown below. Assume
ID: 3202768 • Letter: E
Question
Example: A system consists of three components connected as shown below. Assume that A, B, and C function independently. (Show your work for each problem.)
a. What is the probability that the system functions if each component fails with probability 0.1?
b. If the probabilities that A, B, and C fail are 0.1, 0.05, and 0.2, respectively, what is the probability that the system functions?
c. If components A, B, and C each has probability p of failing, what value must the value of p be so that the system functions with probability 0.99? You will probably need to approximate the answer with the aid of a calculator or computer (not difficult). Round your answer to three decimal places!
A B CExplanation / Answer
a. Let probability of A and B functioning together be Pab. Then Pab = 0.9*0.9 = 0.81
Probability of system functioning = 1 - P(C fails)*P(A and B together do not function) = 1-0.1*(1-0.81) = 0.981
b. Let probability of A and B functioning together be Pab. Then Pab = 0.9*0.95 = 0.855
Probability of system functioning = 1 - P(C fails)*P(A and B together do not function) = 1-0.2*(1-0.855) = 0.971
c. Using the same logic as used in parts a and b,
P(system functions) = 1 - p*(1-p^2) = 1 - p + p^3 = 0.99
Solving above for p gives, p = 0.01
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