The probability is 1% that an electrical connector that is

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Problem 123E Chapter 2.5

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 123E Problem 123E

The probability is 1% that an electrical connector that is kept dry fails during the warranty period of a portable computer. If the connector is ever wet, the probability of a failure during the warranty period is 5%. If 90% of the connectors are kept dry and 10% are wet, what proportion of connectors fail during the warranty period?

Step-by-Step Solution:

Answer

Step 1 of 1</p>

(a)

The probability is  that an electrical connector that is kept dry fails during the warranty period of a portable computer.

If the connector that is ever wet, the probability of a failure during the warranty period is .

If  of the connectors are kept dry and  are wet, what proportion of connectors fail during the warranty period?

Let  denote the event that a connector fails.

Let  denote the event that a connector is wet.

According to the question, we need to find the probability of connector fails given that connector is either wet or  dry.

Based on the total probability rule, we can write,

Assume events  are  mutually exclusive and exhaustive sets meaning independent event. Then

……..(1)

Equation (1) can be modified using the formula of conditional probability,

We can write the conditional probability of  given that  has occurred.

Hence,

Step 2 of 3

Chapter 2.5, Problem 123E is Solved
Step 3 of 3

Textbook: Applied Statistics and Probability for Engineers
Edition: 6th
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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