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

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(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,