# Mathematics

1. Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve” depicts the probability density function for accidents along this stretch:

a) What is the probability that an accident occurred in the first mile along this stretch of highway?

b) What is the probability that an accident did *not* occur in the first mile?

c) What is the probability that an accident occurred between miles 2.5 and 4?

2. Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.

a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?

b) If we randomly select two women from the population who then become pregnant, what is the probability that the first woman’s child will be a boy and the second woman’s child will be a boy?

c) If we randomly select two women from the population who then become pregnant, what is the probability that both children will be boys given that at least one child is a boy?

3. Explain the difference between mutually exclusive and independent events.

4. Suppose a screening test has a sensitivity of 0.80 and a false-positive rate of 0.02. The test is used on a population that has a disease prevalence of 0.007. Find the probability of having the disease given a positive test result.