The probability is 1% that an electrical connector that is

Chapter 2, Problem 123E

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QUESTION:

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?

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QUESTION:

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?

ANSWER:

Step 1 of 2

(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.

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