Q 11.

(a) In a certain population, 10% of the people can be classified as being high risk for a heart attack.Three people are randomly selected from this population. What is the probability that exactly one of the three are high risk?

(b) Suppose we have additional information in the previous example. We know that only 49% of the population are female. Also, of the female patients, 8% are high risk. A single person is selected at random. What is the probability that it is a high risk female?

Q 12. Tom and Dick are going to take a driver's test at the nearest DMV office. Tom estimates that his chances to pass the test are 70% and Dick estimates his as 80%. Tom and Dick take their tests independently.

(a) What is the probability that at most one of the two friends will pass the test?

(b) What is the probability that at least one of the two friends will pass the test?

(c) Suppose we know that only one of the two friends passed the test. What is the probability that it was Dick?