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Concept explainers
Purchasing Sweaters During a sale at a men’s store, 16 white sweaters, 3 red sweaters, 9 blue sweaters, and 7 yellow sweaters were purchased. If a customer is selected at random, find the
a. A blue sweater
b. A yellow or a white sweater
c. A red, a blue, or a yellow sweater
d. A sweater that was not white
a.
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To find: The probability that the randomly selected customer bought a blue sweater.
Answer to Problem 4.2.12RE
The probability that the randomly selected customer bought a blue sweater is 0.257.
Explanation of Solution
Given info:
In the sale of men’s store, 16 white sweaters, 3 red sweaters, 9 blue sweaters and 7 yellow sweaters were purchased.
Calculation:
Let event A denote the customer bought a blue sweater.
The number of blue sweaters are 9.
The total number of sweaters is obtained as follows,
The probability that the randomly selected customer bought a blue sweater is represented by
The formula for obtaining the probability that the randomly selected customer bought a blue sweater is,
Substitute 9 for ‘Number of blue sweaters’ and 35 for ‘Total number of sweaters’
Thus, the probability that the randomly selected customer bought a blue sweater is 0.257.
b.
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To find: The probability that the randomly selected customer bought a yellow or a white sweater.
Answer to Problem 4.2.12RE
The probability that the randomly selected customer bought a yellow or a white sweater is 0.657.
Explanation of Solution
Calculation:
Let event A denote the customer bought a yellow sweater and the event B denote the customer bought a white sweater.
The number of yellow sweaters are 7, number of white sweaters are 16 and total number of sweaters is 35.
The probability that the randomly selected customer bought a yellow or a white sweater is represented by
The formula to obtain the probability that the randomly selected customer bought a yellow or a white sweater is,
The formula to obtain
Substitute 7 for ‘Number of yellow sweaters’ and 35 for ‘Total number of sweaters’
The formula to obtain
Substitute 16 for ‘Number of yellow sweaters’ and 35 for ‘Total number of sweaters’
Substitute 0.2 for
Thus, the probability that the randomly selected customer bought a yellow or a white sweateris 0.657.
c.
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To find: The probability that the randomly selected customer bought a red, a blue or a yellow sweater.
Answer to Problem 4.2.12RE
The probability that the randomly selected customer bought a red, a blue or a yellow sweater is 0.543.
Explanation of Solution
Calculation:
Let event A denote the customer bought a red sweater, the event B denote the customer bought a blue sweater and the event C denote the customer bought a yellow sweater.
The number of red sweaters are 3, number of blue sweaters are 9, number of yellow sweaters are 7 and total number of sweaters are35.
The probability that the randomly selected customer bought a red, a blue or a yellow sweater is represented by
The formula to obtaining the probability that the randomly selected customer bought a red, a blue or a yellow sweater is,
The formula to obtain
Substitute 3 for ‘Number of red sweaters’ and 35 for ‘Total number of sweaters’
The formula to obtain
Substitute 9 for ‘Number of blue sweaters’ and 35 for ‘Total number of sweaters’
The formula to obtain
Substitute 7 for ‘Number of blue sweaters’ and 35 for ‘Total number of sweaters’
Substitute 0.086for
Thus, the probability that the randomly selected customer bought a red, a blue or a yellow sweater is 0.543.
d.
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To find: The probability that the randomly selected customer bought a sweater that is not white.
Answer to Problem 4.2.12RE
The probability that the randomly selected customer bought a sweater that is not white is 0.543.
Explanation of Solution
Calculation:
Let event A denote the customer bought a sweater that is white and the event
The number of white sweaters is 16 and total number of sweaters is 35.
The probability that the randomly selected customer bought a sweater that is not white is represented by
The formula to obtain the probability that the randomly selected customer bought a sweater that is not white is,
The formula to obtain
Substitute 16 for ‘Number of white sweaters’ and 35 for ‘Total number of sweaters’
Substitute 0.457 for
Thus, the probability that the randomly selected customer bought a sweater that is not white is 0.543.
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Chapter 4 Solutions
Elementary Statistics: A Step-by-Step Approach with Formula Card
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