Use the method of natural frequencies to calculate the probabilities.
1. Rework Exercise 3, starting with a class size of 50 people.
Refer to Exercise 3,
The enrollment in a certain course is 10% first-year students, 30% sophomores, 40% juniors, and 20% seniors. Experience has shown that the likelihood of receiving an A in the course is .2 for first-year students, .4 for sophomores, .3 for juniors, and .1 for seniors. Find the probability that a student who receives an A is a sophomore.
2. Rework Exercise 6, starting with 100 people.
Refer to Exercise 6,
Table 6 gives the distribution of voter registration and voter turnouts for a certain city. A randomly chosen person is questioned at the polls. What is the probability that the person is an Independent?
Table 6

3. Rework Exercise 7, starting with a class size of 25 people.
Refer to Exercise 7,
In a calculus course, the instructor gave an algebra exam on the first day of class to help students determine whether or not they had enrolled in the appropriate course. Eighty percent of the students in the class passed the exam. Forty percent of those who passed the exam on the first day of class earned an A in the course, whereas only twenty percent of those who failed the exam earned an A in the course. What is the probability that a student selected at random passed the exam on the first day of class, given that they earned an A in the course?
4. Rework Exercise 12(a), starting with 1000 people.
Refer to Exercise 12,
A drug-testing laboratory produces false negative results 2% of the time and false positive results 5% of the time. Suppose that the laboratory has been hired by a company in which 10% of the employees use drugs.
(a) If an employee tests positive for drug use, what is the probability that they actually use drugs?
(b) What is the probability that a nondrug user will test positive for drug use twice in a row?
(c) What is the probability that someone who tests positive twice in a row is not a drug user?
Refer to diagnostic tests. A false negative in a diagnostic test is a test result that is negative even though the patient has the condition. A false positive, on the other hand, is a test result that is positive although the patient does not have the condition?

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Proportion of Turnout Proportion Registered .50 .4 Democrat Republican .5 20 .7 Independent