CH4_PPT EXAMPLES

# CH4_PPT EXAMPLES - Chapter 4 Probability and Counting Rules...

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Chapter 4 Probability and Counting Rules Section 4-2 Sample Spaces and Probability Exercise #13

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If two dice are rolled one time, find the probability of getting these results. a. A sum of 6 b. Doubles c. A sum of 7 or 11 d. A sum greater than 9 e. A sum less than or equal to 4
a. A sum of 6 There are 6 2 or 36 outcomes. That is because we have 6 outcomes on the first die and 6 outcomes on the second die. 6*6=36 OR We can list the outcomes and count them. 1, 1 2,1 3,1 4,1 5,1 6,1 1, 2 2,2 3,2 4,2 5,2 6,2 1, 3 2,3 3,3 4,3 5,3 6,3 1, 4 2,4 3,4 4,4 4,5 4,6 1, 5 2,5 3,5 4,5 5,5 5,6 1, 6 2,6 3,6 4,6 5,6 6,6 These give us a total of 36 outcomes.

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a. A sum of 6 There are 5 ways to get a sum of 6. They are (1,5), (2,4), (3,3), (4,2), and (5,1). The probability then is 5 36 . Total of 36 outcomes
a. Doubles There are six ways to get doubles. They are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). The probability is then 6 36 = 1 6 . Total of 36 outcomes

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a. A sum of 7 or 11 There are six ways to get a sum of 7. They are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The probability then is 8 36 = 2 9 . Total of 36 outcomes There are two ways to get a sum of 11. They are (5,6) and (6,5).
a. A sum of greater than 9 To get a sum greater than nine, one must roll a 10, 11, or 12. The probability then is 6 36 = 1 6 . Total of 36 outcomes There are six ways to get a 10, 11, or 12. They are (4,6), (5,5), (6,4), (6,5), (5,6), and (6,6).

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a. A sum less than or equal to 4 To get a sum less than or equal to four, one must roll a 4, 3, or 2. The probability then is 6 36 = 1 6 . Total of 36 outcomes There are six ways to get a 4, 3, or 2. They are (3,1), (2,2), (1,3), (2,1), (1,2), and (1,1).
Chapter 4 Probability and Counting Rules Section 4-2 Sample Spaces and Probability Exercise #17

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a. What is the probability that the student is going to graduate school? b. What is the probability that the student is going to medical school? c. What is the probability that the student will have to start paying back his deferred student loans after 6 months (i.e. does not continue in school)? In a college class of 250 graduating seniors, 50 have jobs waiting, 10 are going to medical school, 20 are going to law school, and 80 are going to various other kinds of graduate schools. Select one graduate at random.
P (graduate school) = 110 250 = 11 25 or 0.44 a. What is the probability that the student is going to graduate school? In a college class of graduating seniors, 50 have jobs waiting, 10 are going to medical school, 20 are going to law school, and 80 are going to various other kinds of graduate schools. Select one graduate at random. 10 medical school + 20 law school + 80 various graduate schools = 110

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b. What is the probability that the student is going to medical school? P (medical school) = 10 250 = 1 25 or 0.04 In a college class of graduating seniors, 50 have jobs waiting, are going to medical school, 20 are going to law school, and 80 are going to various other kinds of graduate schools. Select one graduate at random.
c. What is the probability that the student will have to start paying back his deferred student loans after 6 months (i.e. does not continue in school)?

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CH4_PPT EXAMPLES - Chapter 4 Probability and Counting Rules...

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