Compute At-Least Probabilities

question 163

Multiple Choice

Compute At-least Probabilities
-A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.9, P(C) = 0.96, and P(D) = 0.98. Find the probability that at least one of the four parts will work.

• A) 0.999992
• B) 0.762048
• C) 0.000008
• D) 0.237952

---

Definitions:

Indirect Manufacturing Cost

Costs that are not directly traceable to specific units produced, such as utilities or rent for manufacturing facilities.

Relevant Range

The scope of activity within which the assumptions about fixed and variable cost behaviors hold true.

Direct Costs

Expenses that can be directly attributed to the production of specific goods or services.

Indirect Manufacturing Cost

Costs not directly associated with the production of goods, including maintenance, supervision, and utility expenses.