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 1

1.4% of connectors fail during the warranty period.

Explanation:

We have these following probabilities:

A 90% probability that a connector is kept dry.

A 10% probability that a connectors is wet.

If a connector is dry, an 1% probability of failling.

If a connector is wet, a 5% probability of failling.

What proportion of connectors fail during the warranty period?

This is 1% of 90% and 5% of 10%. So

`P = 0.01*0.9 + 0.05*0.1 = 0.014`

1.4% of connectors fail during the warranty period.