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? Let: D = electrical connector is dry D' = electrical connector is not kept dry (i.e., is wet) F = connector fails during warranty period F' = connector does not fail during warranty period Match the correct probability description to each given probability value

Answer 1

0.014 or 1.4% of connectors fail during the warranty period.

Explanation:

Consider the provided information.

Let: D = electrical connector is dry

D' = electrical connector is not kept dry (i.e., is wet)

F = connector fails during warranty period

F' = connector does not fail during warranty period

90% of the connectors are kept dry

That means P(D)=0.9

10% are wet,

P(D')=0.1

The probability is 1% that an electrical connector that is kept dry fails during the warranty period, i.e.

P(F|D)=0.01

If the connector is ever wet, the probability of a failure during the warranty period is 5%, i.e.

P(F|D')=0.05

`P(F)=P(D)* P(F|D)+P(D')* P(F|D')\\P(F)=0.9* 0.01+0.1* 0.05\\P(F)=0.014`

Hence, 0.014 or 1.4% of connectors fail during the warranty period.