00:01
For random breathalyzer tests, we are told that the overall probability of testing positive is 3%, and that 9 out of 1 ,000 drivers are drunk, so that probability is 0 .009.
00:17
And we are also told that the breathalyzer test always detects a drunk person.
00:21
So the probability of testing positive, given that the person is drunk, is 1.
00:28
Here we are asked for the probability that the driver is not drunk and we get a positive test.
00:39
Now using probability theory, this is equal to the probability of testing positive given that the driver is not drunk, times the probability of the driver not being drunk.
00:52
So this probability is pretty straightforward to solve.
00:57
The probability that the driver is not drunk.
01:00
Well, this event is the complement of the driver being drunk, so it's 1 minus 0 .0 .0 .3.
01:06
0 .991.
01:13
And now for this probability, we can make use of the law of total probability...