1. Do problem 92 on page 71. Answer = _________. Hint: There are 16 outcomes in

Question

1. Do problem 92 on page 71. Answer = _________.    Hint: There are 16 outcomes in the sample space with regards to the components working or not working. These are not equally likely. Identify which of the 16 denote a “working” system, compute their probabilities using the multiplicative law, and add them up.

2. Refer to the previous problem. Given that the system works, compute the probability that component B is working.
Answer = _________.    Hint: Use the formula for conditional probability.

Explanation / Answer

1) P(system works) = P(A, B and D workling, C not working) + P(A, C, D working, B not working) + P(A,B,C and D working)

= 0.95x0.7x0.2x0.9 + 0.95x0.3x0.8x0.9 + 0.95x0.7x0.8x0.9

= 0.1197 + 0.2052 + 0.4788

= 0.8037

2) P(B is working | system working) = P(B working and system working)/ P(system working)

=  (0.95x0.7x0.2x0.9 + 0.95x0.7x0.8x0.9)/0.8037

= 0.7447

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