(a)
To find:
The probability that Mrs. Harvey selects a male, given that she chooses from only the sophomores.
(a)
Answer to Problem 17E
Solution:
The required probability is 0.444.
Explanation of Solution
Given information:
Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.
Mrs. Harvey’s Algebra Class | ||
Male | Female | |
Freshman | 9 | 13 |
Sophomore | 4 | 5 |
Junior | 4 | 2 |
Senior | 2 | 3 |
Definition:
Dependent
Two events are dependent if one event happening effect the probability of the other event happening.
Formula used:
If
Calculation:
Total number of student is 42.
There are 4 male and 5 female sophomores.
Total number of sophomore is 9.
Let
Calculate the probability of event
Calculate the probability of event
Use the formula to calculate the conditional probability of event
Conclusion:
Thus, the probability that Mrs. Harvey selects a male, given that she chooses from only the sophomores is 0.444.
(b)
To find:
The probability that Mrs. Harvey selects a junior, given that she chooses a female.
(b)
Answer to Problem 17E
Solution:
The required probability is 0.0870.
Explanation of Solution
Given information:
Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.
Mrs. Harvey’s Algebra Class | ||
Male | Female | |
Freshman | 9 | 13 |
Sophomore | 4 | 5 |
Junior | 4 | 2 |
Senior | 2 | 3 |
Definition:
Dependent Event:
Two events are dependent if one event happening effect the probability of the other event happening.
Formula used:
If
Calculation:
Total number of student is 42.
There are 4 male and 2 female junior.
Total number of junior is 6.
Total number of female is
Let
Calculate the probability of event
Calculate the probability of event
Use the formula to calculate the conditional probability of event
Conclusion:
Thus, the probability that Mrs. Harvey selects a junior, given that she chooses a female is 0.0870.
(c)
To find:
The probability that Mrs. Harvey selects a female, given that she chooses a junior.
(c)
Answer to Problem 17E
Solution:
The required probability is 0.333.
Explanation of Solution
Given information:
Mrs. Harvey’s algebra class has 42 students, classified by academic year and gender as follows.
Mrs. Harvey’s Algebra Class | ||
Male | Female | |
Freshman | 9 | 13 |
Sophomore | 4 | 5 |
Junior | 4 | 2 |
Senior | 2 | 3 |
Definition:
Dependent Event:
Two events are dependent if one event happening effect the probability of the other event happening.
Formula used:
If
Calculation:
Total number of student is 42.
There are 4 male and 2 female junior.
Total number of junior is 6.
Total number of female is
Let
Calculate the probability of event
Calculate the probability of event
Use the formula to calculate the conditional probability of event
Conclusion:
Thus, the probability that Mrs. Harvey selects a female, given that she chooses a junior is 0.333.
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Chapter 4 Solutions
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