An individual suspected of driving under the influence of alcohol may be given a

Question

An individual suspected of driving under the influence of alcohol may be given a “rapid test” which has the probability of .75 of being correct. Assume that 60% of the drivers stopped for being suspected of driving under the influence of alcohol actually are. The other 40% are just sleepy or texting on their cell phones.

If this test gives a positive result, the individual is subjected to a further test that detects a DUI with a 90% chance of being accurate. It is 100% accurate for those having an alcohol content below the legal limit. Assume the two tests are independent.

A) What proportion of subjects will pass the second test?

B) What is the probability that a suspect with alcohol content above the legal limit will pass the second test?

C) What proportion of subjects are not given the second test?

Explanation / Answer

a) Proportion of people pasing the second test will be found from the people who take it.

Number of people who are subjected to the test = 0.75*0.6+ 0.25*0.4 = 0.55

In this, 45 are actually under alcohol and 10 are not

Proportion passing the test = 10/55*1+45/55*0.1 = 0.2636

b)P( Alcohol content person passing) = 45/55*0.1 / 0.2636 = 4.5/14.5 = 0.3103

c) Subjects not given the second tet = 1-0.55=0.45

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