Chapter Test 185 Chapter Test 3 Take this test as you would take a test in class. 1. Your dorm enters 15 out of 65 plastic numbered ducks in a duck race. The ducks are all dumped into a stream and drift to the finish line. What is the probability that three of your dorm’s ducks finish first, second, and third? 2. A person’s building access code is their first and last initials and four digits. (a) What is the probability of randomly guessing a person’s access code in one try? (b) What is the probability that a random try does not give the person’s access code? (c) You know a person’s first name only, and you know that the last digit is odd. What is the probability of guessing this person’s code on the first try? (d) Are the statements in parts (a)–(c) examples of classical probability, empirical probability, or subjective probability? Explain your reasoning. 3. Determine whether the events are mutually exclusive. Explain your reasoning. Event A: Randomly select a student born on the 30th of a month Event B: Randomly select a student with a birthday in February 4. The table on the left shows the secondary school student enrollment levels (in thousands by grade) in Oklahoma and Texas schools in a recent year. (Source: U.S. National Center for Education Statistics) A student in one of the indicated grades and states is randomly selected. Find the probability of selecting a student who (a) is in ninth grade. (b) is in ninth or tenth grade. (c) is in eleventh grade, given that the student is enrolled in Oklahoma. (d) is enrolled in Texas, given that the student is in twelfth grade. (e) is in eleventh grade or is enrolled in Oklahoma. (f) is in twelfth grade and is enrolled in Oklahoma. 5. Which event(s) in Exercise 4 can be considered unusual? Explain your reasoning. 6. A person is selected at random from the sample in Exercise 4. Are the events “the student is in ninth grade” and “the student is enrolled in Texas” independent or dependent? Explain your reasoning. 7. There are 16 students giving final presentations in your history course. (a) Three students present on the first day. How many presentation orders are possible for the first day? (b) Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on the same unit are indistinguishable from each other? Oklahoma Texas Total Ninth grade 52.3 437.2 489.5 Tenth grade 50.4 401.2 451.6 Eleventh grade 46.7 373.4 420.1 Twelfth grade 44.1 353.3 397.4 Total 193.5 1565.1 1758.6 TABLE FOR EXERCISE 4
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