Question

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: 5 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser as being above the legal limit, while 15 % of drivers who are above the legal limit will give a reading below that level. Suppose that in fact 12 % 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.

a. What is the probability that the driver is incorrectly classified as being over the limit?
b. What is the probability that the driver is correctly classified as being over the limit?
c. Find the probability that the driver gives a breathalyser test reading that is over the limit.
d. Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.

Answer 1

It can be deduced that the probability that the driver is incorrectly classified is 0.044.

How to calculate probability

From the information, 12 % of drivers are above the legal alcohol limit. Those below the legal alcohol limit will be:

= 1 - 0.12 = 0.88

Therefore, the probability that the driver is incorrectly classified as being over the limit will be:

= 0.05 × 0.88

= 0.044.

The the probability that the driver is correctly classified as being over the limit will be:

= P(B/A) × P(A)

= 0.85 × 0.12

= 0.102

The probability that the driver gives a breathalyser test reading that is over the limit will be:

= 0.85 × 0.12 × 0.05 × 0.88

= 0.146

Lastly, the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit will be:

= (0.88 × 0.95) / (0.88 × 0.95 + 0.12 × 0.15)

= 0.98

Learn more about probability on:

https://brainly.com/question/25870256