Suppose a breathalyzer has 5 false positives and 8 false neg

Suppose a breathalyzer has 5% false positives and 8% false negatives. That is, only 5% of the time will it indicate that a person is drunk when he is actually sober and 8% of the time will it indicate that a person is sober when the person is in fact drunk. Using this test, the police spot test a population of drivers, 99% of whom are sober. What is the chance that a person, who tests as drunk, is actually sober?

Could you show me the solutions steps

Solution

What is the chance that a person, who tests as drunk, is actually sober?

we have the population of drivers that are sober

so we just need to do a multiplication

multiply the population of sober 0.99 by the time will it indicate that a person is drunk when he is actually sober that is 0.05

0.99 * 0.05 = 0.0495