In: Statistics and Probability
A breathalyser test is used by police in an area to determine
whether a driver has an excess of alcohol in their blood. The
device is not totally reliable: 7 % of drivers who have not
consumed an excess of alcohol give a reading from the breathalyser
as being above the legal limit, while 10 % of drivers who are above
the legal limit will give a reading below that level. Suppose that
in fact 14 % of drivers are above the legal alcohol limit, and the
police stop a driver at random. Give answers to the following to
four decimal places.
Part a)
What is the probability that the driver is incorrectly classified
as being over the limit?
Part b)
What is the probability that the driver is correctly classified as
being over the limit?
Part c)
Find the probability that the driver gives a breathalyser test
reading that is over the limit.
Part d)
Find the probability that the driver is under the legal limit,
given the breathalyser reading is also below the limit.