Homework SourseSample problems related to texts Chapter 4 22 Give examples
| 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 |
Solution
(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.
---------------------------------------------------------------------------------------------------------------
(23)(a) (1,5), (1,6), (5,6)
(5,1), (6,1), (6,5)
----------------------------------------------------------------------------------------------------
(b) P(A)= 4/6 =0.6666667
----------------------------------------------------------------------------------------------------
(c) P(B)=2/6=0.3333333
----------------------------------------------------------------------------------------------------
(d) P(A&B)=0/6=0
----------------------------------------------------------------------------------------------------
(e) P(A or B)= P(A)+P(B)- P(A and B)
=4/6 + 2/6 -0
=1
----------------------------------------------------------------------------------------------------
(f)P(A given B)= P(A and B)/P(B)
=0
----------------------------------------------------------------------------------------------------
(g)P(not B)= 1-P(B)
=1-2/6
=4/6 =0.6666667
----------------------------------------------------------------------------------------------------
(h) Yes, events A and B are mutually exclusive because P(A and B)=0
---------------------------------------------------------------------------------------------------------------
(24)(a) Non of ten of the patients seen today had some infectious disease.
----------------------------------------------------------------------------------------------------
(b)All of the patients seen today had no infectious disease.
---------------------------------------------------------------------------------------------------------------
(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 |
