Police report that 88% of drivers stopped on suspicion of
drunk driving are given a breath test, 15% a blood test, and 10% both tests.
What is the probability that the next driver stopped on suspicion of drunk
driving is given:
i) at least one of the tests?
ii) a blood test or a breath test, but not both?
iii) neither test?
vi) Consider the two events "given a blood test" and "given a breath test".
(a) Are the events mutually exclusive?
(b) Are the events independent?
Draw a Venn diagram and label two overlapping circles in it blood and breath. Breath is .88, blood is .15 and the intersection is .10.
Therefore .88 - .10 = .78 is the nuumber given just the breath test.
Similarly, .15 - .10 = .05 is the nuumber given just the blood test.
Finally, .78 + .10 + .05 = the total given at least one test, and 1 minus that number is the number not given either test.
Since the circles overlap they can't be mutually exclusive.
I'll let you use this for now and work the rest of the questions. Please show some work too.
It says 35+85+443=?
To answer the questions, let's use the information provided in the problem.
i) To find the probability that the next driver stopped on suspicion of drunk driving is given at least one of the tests, we need to find the complement of the probability that the driver is given neither test. From the diagram, we know that the probability of not being given either test is 1 - (0.78 + 0.10 + 0.05).
ii) To find the probability that the next driver stopped on suspicion of drunk driving is given a blood test or a breath test, but not both, we need to find the sum of the probabilities of two exclusive events. From the diagram, we can see that the probability of being given just a blood test is 0.05, and the probability of being given just a breath test is 0.78. So the probability is 0.05 + 0.78.
iii) To find the probability that the next driver stopped on suspicion of drunk driving is given neither test, we mentioned earlier that it is 1 - (0.78 + 0.10 + 0.05).
iv) Now let's consider the two events "given a blood test" and "given a breath test":
(a) The events are not mutually exclusive because there are drivers who are given both tests (10% of the sample).
(b) To determine if the events are independent, we need to check if the probability of one event changes depending on whether the other event has occurred. In this case, the probability of being given a blood test changes depending on whether a breath test has occurred. Therefore, the events are dependent.
As for the final question, to calculate 35 + 85 + 443, we simply add the numbers together, resulting in 563.
Please let me know if there is anything else I can help you with!