Concept explainers
a.
Find
a.
Answer to Problem 88CR
The
Explanation of Solution
Calculation:
The percentage of passengers on a cruise ship who check work e-mail, use a cell phone, bring a laptop, check work e-mail and use a cell phone and neither check work e-mail nor use a cell phone are 40%, 30%, 25%, 23%, and 51%, respectively. The percentage of passengers who bring a laptop and check work e-mail is 88% and the percentage of passengers who use a cell phone and bring a laptop is 70%.
The events that a traveler on leave checks work e-mail, uses a cell phone, and bring a laptop are denoted as E, C, and L, respectively.
The given information is the summary table of the survey.
The probability of any Event A is given below:
Here, the percentage of passengers on a cruise ship who check work e-mail is 40%.
Thus, the probability of the event that a traveler on vacation on a cruise ship who checks work e-mail is 0.4.
b.
Obtain
b.
Answer to Problem 88CR
The probability of the event that a traveler on vacation on a cruise ship who uses a cell phone is 0.3.
Explanation of Solution
Calculation:
Here, the percentage of travelers on vacation on a cruise ship who uses a cell phone is 30%.
Thus, the probability of the event that a passenger on a cruise ship who uses a cell phone is 0.3.
c.
Compute
c.
Answer to Problem 88CR
The probability of the event that a passenger on a cruise ship who brought a laptop is 0.25.
Explanation of Solution
Calculation:
Here, the percentage of passengers on a cruise ship who brought a laptop is 25%.
Thus, the probability of the event that a traveler on vacation on a cruise ship who brought a laptop is 0.25.
d.
Calculate
d.
Answer to Problem 88CR
The probability of the event that a traveler on a cruise ship who checks work e-mail and uses a cell phone is 0.23.
Explanation of Solution
Calculation:
Here, the percentage of passengers on a cruise ship who checks work e-mail and uses a cell phone is 23%.
Thus, the probability of the event that a passenger on a cruise ship who checks work e-mail and uses a cell phone is 0.23.
e.
Calculate
e.
Answer to Problem 88CR
The probability of the event that a passenger on a cruise ship neither checks work e-mail nor uses a cell phone nor bring a laptop is 0.51.
Explanation of Solution
Calculation:
Here, the percentage of travelers on a cruise ship neither checks work e-mail nor uses a cell phone nor bring a laptop is 51%.
Thus, the probability of the event that a passenger on a cruise ship neither checks work e-mail nor uses a cell phone nor bring a laptop is 0.51.
f.
Compute
f.
Answer to Problem 88CR
Explanation of Solution
Calculation:
The given information is about the percentage of passengers on a cruise ship who checks work e-mail, use a cell phone, bring a laptop, check work e-mail and use a cell phone, and neither check work e-mail nor use a cell phone nor bring a laptop are 40%, 30%, 25%, 23%, and 51%, respectively. The percentage of passengers who bring a laptop also check work e-mail is 88% and those who use a cell phone and bring a laptop is 70%.
The events that a passenger checks work e-mail, uses a cell phone, and brought a laptop are denoted as E, C, and L, respectively.
The required probability can be obtained as follows:
The general formula for
Here, the percentage passengers who neither check work e-mail nor use a cell phone nor bring a laptop is 51%.
Then, the probability of passengers who check work e-mail nor use a cell phone nor bring a laptop is 0.49
Therefore,
The given probability values are as follows:
The probability of passengers who bring a laptop also checks work e-mail
The probability of passengers who check work e-mail and brings a laptop is obtained as follows:
Thus,
The probability of passengers who uses a cell phone and brings a laptop is obtained as follows:
Thus,
Then, the probability that a passenger on a cruise ship who checks work e-mail, uses a cell phone and brings a laptop is given below:
Thus,
The required probability is given below:
Thus,
g.
Obtain
g.
Answer to Problem 88CR
Explanation of Solution
It is known that 88% of the passengers who brought laptops also checks work e-mail. Therefore,
h.
Find
h.
Answer to Problem 88CR
Explanation of Solution
It is known that 70% of the passengers who uses a cell phone also brought a laptop. Therefore,
i.
Find
i.
Answer to Problem 88CR
The value of
Explanation of Solution
Calculation:
The percentage of passengers on a cruise ship who check work e-mail, use a cell phone, bring a laptop, check work e-mail and use a cell phone, and neither check work e-mail nor use a cell phone nor bring a laptop are 40%, 30%, 25%, 23%, and 51%, respectively. The percentage of passengers who bring a laptop also check work e-mail is 88% and use a cell phone also bring a laptop is 70%.
The events that a passenger checks work e-mail, uses a cell phone, and brought a laptop are denoted as E, C, and L, respectively.
The general formula for
Then, the formula for the required probability is as follows:
Here, the percentage passengers who neither check work e-mail nor use a cell phone nor bring a laptop is 51%.
Then, the probability of passengers who check work e-mail nor use a cell phone nor bring a laptop is
The probability of passengers, who check work e-mail is 0.40.
The probability of passengers who use a cell phone is 0.30.
The probability of passengers who bring a laptop is 0.25.
The probability of passengers who bring a laptop also check work e-mail is 0.88.
The probability of passengers who check work e-mail and bring a laptop is obtained as follows:
Thus, the probability of passengers who check work e-mail and bring a laptop is 0.22.
The probability of passengers who use a cell phone also bring a laptop is 0.7.
The probability of passengers who use a cell phone and bring a laptop is obtained as follows:
Thus, the probability of passengers who use a cell phone and bring a laptop is 0.21.
Then, the probability of the event that a passenger on a cruise ship who check work e-mail, use a cell phone, and bring a laptop is given below:
Thus, the probability of the event that a passenger on a cruise ship who check work e-mail, use a cell phone, and bring a laptop is 0.2.
j.
Obtain
j.
Answer to Problem 88CR
The probability of the event that a passenger on a cruise ship who check e-mail and bring a laptop is 0.22.
Explanation of Solution
From Part (a), the probability of passengers who check work e-mail and bring a laptop is 0.22.
k.
Obtain
k.
Answer to Problem 88CR
The probability of the event that a passenger on a cruise ship who use a cell phone and bring a laptop is 0.21.
Explanation of Solution
From Part (a), the probability of passengers who use a cell phone and bring a laptop is 0.21.
l.
Calculate
l.
Answer to Problem 88CR
The probability of the event that a passenger uses a cell phone, given that he or she checks work e-mail and brought a laptop is 0.909.
Explanation of Solution
Calculation:
Conditional rule:
The formula for probability of E given F is
Then, the required probability can be obtained as follows:
From Part (a),
Thus, the probability of the event that a passenger uses a cell phone, given that he or she checks work e-mail, and brought a laptop is 0.909.
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Chapter 6 Solutions
Introduction to Statistics and Data Analysis
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