Sample problems related to text\'s Chapter 4 22. Give examples of two different

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Sample problems related to text's Chapter 4 22. Give examples of two different numbers that can be used to represent a probability value. Then, give examples of two numbers that can never represent a probability value. Explain why the last two values you gave cannot represent a probability value. 23. Consider the situation where you have three game chips, each labeled with one of the the numbers 1,5,& 6 in a hat: a. If you draw out 2 chips without replacement between each chip draw, list the entire sample space of possible results that can occur in the draw. Define two events as follows for answering parts b to h below: Event A: the sum of the 2 drawn numbers is odd. Event B: the sum of the 2 drawn numbers is a multiple of 3. Now, using your answer to part a. find the following probability values: b. P(A)= c. P(B)= d. P(A&B)= e. P(A or B)= f. P(A given B)= g. P(not B)= h. Are events A and B mutually exclusive? Why or why not? 24. Provide a written description of the complement of each of the following: a. At least ten of the patients seen today had some infectious disease. b. All of the patients seen today had some infectious disease. 25 A researcher recorded the amount of time each patron at a fast food restraunt spent waiting in line for service during noontime Saturday. The frequency table at the right summarizes the data collected. First, extend the table to include a relative frequency column. Then, if we randomly select one of the patrons represented in the table, what is the proabability that the waiting time is at least 12 minutes? Wating Time (Minutes) Number of
Customers Relative Frequency: 0-3 8 4-7 15 8-11 22 12-15 14 16-19 5 20-23 2 Sample problems related to text's Chapter 4 22. Give examples of two different numbers that can be used to represent a probability value. Then, give examples of two numbers that can never represent a probability value. Explain why the last two values you gave cannot represent a probability value. 23. Consider the situation where you have three game chips, each labeled with one of the the numbers 1,5,& 6 in a hat: a. If you draw out 2 chips without replacement between each chip draw, list the entire sample space of possible results that can occur in the draw. Define two events as follows for answering parts b to h below: Event A: the sum of the 2 drawn numbers is odd. Event B: the sum of the 2 drawn numbers is a multiple of 3. Now, using your answer to part a. find the following probability values: b. P(A)= c. P(B)= d. P(A&B)= e. P(A or B)= f. P(A given B)= g. P(not B)= h. Are events A and B mutually exclusive? Why or why not? 24. Provide a written description of the complement of each of the following: a. At least ten of the patients seen today had some infectious disease. b. All of the patients seen today had some infectious disease. 25 A researcher recorded the amount of time each patron at a fast food restraunt spent waiting in line for service during noontime Saturday. The frequency table at the right summarizes the data collected. First, extend the table to include a relative frequency column. Then, if we randomly select one of the patrons represented in the table, what is the proabability that the waiting time is at least 12 minutes? Wating Time (Minutes) Number of
Customers Relative Frequency: 0-3 8 4-7 15 8-11 22 12-15 14 16-19 5 20-23 2

Explanation / Answer

(22) A probability value must be 0 and 1.

For example, two different numbers that can be used to represent a probability value are 0.2 and 0.3

For example, two numbers that can never represent a probability value are -1 and -0.2.

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(23)(a) (1,5), (1,6), (5,6)

(5,1), (6,1), (6,5)

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(b) P(A)= 4/6 =0.6666667

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(c) P(B)=2/6=0.3333333

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(d) P(A&B)=0/6=0

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(e) P(A or B)= P(A)+P(B)- P(A and B)

=4/6 + 2/6 -0

=1

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(f)P(A given B)= P(A and B)/P(B)

=0

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(g)P(not B)= 1-P(B)

=1-2/6

=4/6 =0.6666667

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(h) Yes, events A and B are mutually exclusive because P(A and B)=0

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(24)(a) Non of ten of the patients seen today had some infectious disease.

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(b)All of the patients seen today had no infectious disease.

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(25) the proabability that the waiting time is at least 12 minutes is

P(X>12) =(14+5)/64 =0.296875

Wating Time Number of Customer Relative Frequency 0 to 3 8 0.125 4 to 7 15 0.234375 8 to 11 22 0.34375 12 to 15 14 0.21875 16 to 19 5 0.078125 Total 64

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