AP Statistics Multiple-Choice Practice Questions: Probability as Relative Frequency 1

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Question 11 questions

Time 25 minutes

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1. A student reasons that either he will or will not receive a 5 on the AP Statistics exam, and therefore the probability of receiving a 5 is 0.5. Why is this incorrect reasoning?

2. In the November 27, 1994, issue of Parade magazine, the "Ask Marilyn" section contained this question: "Suppose a person was having two surgeries performed at the same time. If the chances of success for surgery A are 85%, and the chances of success for surgery B are 90%, what are the chances that both would fail?" What do you think of Marilyn's solution: (0.15)(0.10) = 0.015 or 1.5%?

3. A weighted die comes up spots with the following probabilities:

If two of these dice are thrown, what is the probability the sum is 10?

4. According to a CBS/New York Times poll taken in 1992, 15% of the public have responded to a telephone call-in poll. In a random group of five people, what is the probability that exactly two have responded to a call-in poll?

5. In a 1974 "Dear Abby" letter a woman lamented that she had just given birth to her eighth child, and all were girls! Her doctor had assured her that the chance of the eighth child being a girl was only 1 in 100. What was the real probability that the eighth child would be a girl?

6. The yearly mortality rate for American men from prostate cancer has been constant for decades at about 25 of every 100,000 men. (This rate has not changed in spite of new diagnostic techniques and new treatments.) In a group of 100 American men, what is the probability that at least 1 will die from prostate cancer in a given year?

7. Alan Dershowitz, one of O. J. Simpson's lawyers, has stated that only 1 out of every 1000 abusive relationships ends in murder each year. If he is correct, and if there are approximately 1.5 million abusive relationships in the United States, what is the expected value for the number of people who are killed each year by an abusive partner?

8. For an advertising promotion, an auto dealer hands out 1000 lottery tickets with a prize of a new car worth $25,000. For someone with a single ticket, what is the standard deviation for the amount won?

9. Suppose that among the 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. If taking honors courses and preferring basketball are independent, how many students are both taking honors courses and prefer basketball to football?

10. An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least two of the three items are in perfect condition. If in reality 90% of the whole lot are perfect, what is the probability that the lot will be accepted?

11. Suppose that, in a certain part of the world, in any 50-year period the probability of a major plague is .39, the probability of a major famine is .52, and the probability of both a plague and a famine is .15. What is the probability of a famine given that there is a plague?