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Chapter 4: Problem 101

Terry \& Sons makes bearings for autos. The production system involves two independent processing machines so that each bearing passes through these two processes. The probability that the first processing machine is not working properly at any time is \(.08\), and the probability that the second machine is not working properly at any time is \(.06\). Find the probability that both machines will not be working properly at any given time.

Short Answer

Expert verified
The probability that both machines will not be working properly at any given time is \(0.0048\).

Step by step solution

01

Identify the probabilities of individual events

First, identify the probabilities of individual machines not working properly. It is given that the probability that the first engine not working properly, P(A), is \(0.08\) and the probability of the second engine not working properly, P(B), is \(0.06\).
02

Apply the multiplication rule for independent events

Since the events are independent, directly apply the multiplication rule of probability. This rule states that the probability of both independent events A and B occurring, P(A and B), is given by the product of their individual probabilities, i.e., P(A and B) = P(A) 脳 P(B).
03

Calculate the required probability

Using the given probabilities of individual events, the probability of both machines not working properly is: P(A and B) = \(0.08 脳 0.06 = 0.0048\). This is the final answer.

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