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1. Suppose that, for any given year, the probabilities that the stock market declines, that women's hemlines are lower, and that both events occur are, respectively, 0.4, 0.35, and 0.3. Are the two events independent?
2. If P(A) = 0.2 and P(B) = 0.1, what is P(A ∪ B) if A and B are independent?
3. The following data are from The Commissioner's Standard Ordinary Table of Mortality:
What is the probability that a 20-year-old will survive to be 70?
4. At a warehouse sale 100 customers are invited to choose one of 100 identical boxes. Five boxes contain $700 color television sets, 25 boxes contain $540 camcorders, and the remaining boxes contain $260 cameras. What should a customer be willing to pay to participate in the sale?
5. There are two games involving flipping a coin. In the first game you win a prize if you can throw between 40% and 60% heads. In the second game you win if you can throw more than 75% heads. For each game would you rather flip the coin 50 times or 500 times?
6. During the 2015 season, Anthony Rizzo and Kris Bryant getting hits, one after the other, were independent events. The probability of both getting hits was 0.07645. The probability of Rizzo getting a hit and Bryant not getting a hit was 0.20155. What was the probability of Bryant getting a hit?
7. The average annual incomes of high school and college graduates working at a particular company are $21,000 and $35,000, respectively. If the company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees?
8. An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2, and of having a major accident, 0.05, how much can the insurance company expect to make on a policy?
9. You can choose one of three boxes. Box A has four $5 bills and a single $100 bill, box B has 400 $5 bills and 100 $100 bills, and box C has 24 $1 bills. You can have all of box C or blindly pick one bill out of either box A or box B. Which offers the greatest expected winning?
10. Given that 52% of the U.S. population are female and 15% are older than age 65, can we conclude that (0.52)(0.15) = 7.8% are women older than age 65?
11. Question below refers to the following study: One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
What is the probability that a student has a GPA between 2.0 and 3.0?