Question

Police often set up sobriety checkpoints-roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. if the officer does not suspect a problem, drivers are released to go on their way. otherwise, drivers are detained for a breathalyzer test that will determine whether or not they will be arrested. the police say that based on the brief initial stop, trained officers can make the right decision 66% of the time. suppose the police operate a sobriety checkpoint after 9:00 p.m. on a saturday night, a time when traffic safety experts suspect that about 10% of drivers have been drinking.

A statistics student is stopped at the checkpoint and, of course, has not been drinking. What is the probability that the statistics student is detained for further testing?
a) 0.66
b) 0.34
c) 0.10
d) 0.90

Answer 1

The probability that a sober statistics student is detained for further testing at a sobriety checkpoint, given that officers have a 66% accuracy rate, is 34%.

Step-by-step explanation:

The question asks what the probability is that a non-drinking statistics student is detained for further testing at a sobriety checkpoint, given that trained officers make the right decision 66% of the time, and it is suspected that about 10% of drivers have been drinking.

Since the officers can correctly identify a driver's state 66% of the time, they incorrectly identify the driver's state 34% of the time (100% - 66%). As the student has not been drinking, the only way the student gets detained is if the officers make a wrong decision. Hence, the probability that the statistics student is detained is the same as the probability that an officer makes an incorrect identification, which is 34%.

Therefore, the correct answer is b) 0.34.