In a large national population of college students, 61% attend 4-year institutions and the rest attend...
In a large national population of college students, 61% attend 4-year institutions and the rest attend 2-year institutions. Males make up 44% of the students in the 4-year institutions and 41% of the students in the 2-year institutions.
a. Find the four probabilities for each combination of gender and type of institution using a two-way table.
b. Consider randomly selecting a female student from this population. What is the probability that she attends a 4-year institution?
c. Draw a tree diagram to illustrate the probabilities in a situation where you first identify the type of institution attended and then identify the gender of the student.
d. Draw a different tree diagram to illustrate the probabilities in a situation where you first identify the gender of the student and then identify the type of institution attended. Explain why the probabilities in this tree diagram are different from those that you used in part (c)
Homework Answers
a.
We have 61% of students in 4-year institution.
So, There are 39% of students in 2-Year institution.
Now,
Males in 4-Year institution = 44 % of students in 4-year institution = 0.44 * 0.61 = 0.27
Males in 2-Year institution = 41 % of students in 2-year institution = 0.41 * 0.39 = 0.16
Females in 4-Year institution = (100-44) % of students in 4-year institution = 56 % of students in 4-year institution
= 0.56 * 0.61 = 0.34
Females in 2-Year institution = (100-41) % of students in 2-year institution = 59 % of students in 2-year institution
= 0.59 * 0.39 = 0.23
So, Two-way table for probabilities for each combination of gender and type of institution is :
| 4-year | 2-year | Total | |
| Male | 0.27 | 0.16 | 0.43 |
| Female | 0.34 | 0.23 | 0.57 |
| Total | 0.61 | 0.39 | 1.00 |
b.
The probability that female student from the population attends a 4-year institution = 0.56 * Probability that a student is from 2-Year institution = 0.56 * 0.61 = 0.34
c.
d.
Since, these are
conditional probabilities and Gender and type of institution are
not independent of each other , the probabilities in the tree
diagrams are different.
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