Question 1. Hint: There are 16 outcomes in the sample space with regards to the

Question

Question 1.

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.

Question 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.

2.92 Suppose the diagram of an electrical system is as given in Figure 2.10. What is the probability that the system works? Assume the components fail ide pendently

Explanation / Answer

1) P(system working) = P(A working) x P(B or C working) x P(D working)

= 0.95 x (1 - P(B and C both failing) x 0.9

= 0.95 x (1 - 0.3x0.2) x 0.9

= 0.95 x 0.94 x 0.9

= 0.8037

2) P(system working and component B working) = 0.95x0.7x0.9 = 0.5985

P(B is working | system works) = P(system working and component B working) / P(system works)

= 0.5985/0.8037

= 0.7449

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.