Question

What is the probability that a randomly selected CMSU student will be male?
The Student News Service at Clear Mountain State University (CMSU) has decided to gather data about the undergraduate students that attend CMSU. CMSU creates and distributes a survey of 14 questions and receives responses from 62 undergraduates

What is the probability that a randomly selected CMSU student will be female?
Find the conditional probability of different majors among the male students in CMSU.
Find the conditional probability of different majors among the female students of CMSU.
Find the conditional probability of intent to graduate, given that the student is a male.
Find the conditional probability of intent to graduate, given that the student is a female.
Find the conditional probability of employment status for the male students as well as for the female students.
Find the conditional probability of laptop preference among the male students as well as among the female students.

ID	Gender	Age	Class	Major	Grad Intention	GPA	Employment	Salary	Social Networking	Satisfaction	Spending	Computer	Text Messages
1	Female	20	Junior	Other	Yes	2.9	Full-Time	50	1	3	350	Laptop	200
2	Male	23	Senior	Management	Yes	3.6	Part-Time	25	1	4	360	Laptop	50
3	Male	21	Junior	Other	Yes	2.5	Part-Time	45	2	4	600	Laptop	200
4	Male	21	Junior	CIS	Yes	2.5	Full-Time	40	4	6	600	Laptop	250
5	Male	23	Senior	Other	Undecided	2.8	Unemployed	40	2	4	500	Laptop	100
6	Female	22	Senior	Economics/Finance	Undecided	2.3	Unemployed	78	3	2	700	Laptop	30
7	Female	21	Junior	Other	Undecided	3	Part-Time	50	1	3	500	Laptop	50
8	Female	22	Senior	Other	Undecided	3.1	Full-Time	80	1	2	200	Tablet	300
9	Female	20	Junior	Management	Yes	3.6	Unemployed	30	0	4	500	Laptop	400
10	Female	21	Senior	Economics/Finance	Undecided	3.3	Part-Time	37.5	1	4	200	Laptop	100
11	Female	23	Senior	Economics/Finance	Yes	2.8	Full-Time	50	2	5	400	Laptop	200
12	Male	21	Senior	Undecided	No	3.5	Full-Time	37	2	3	500	Laptop	100

Answer 1

We have a data set consisting of 12 entries. So for all purpose, the sample size is n(S) = 12. This will therefore be the denominator for all problems, unless sample size itself gets changed.

1. What is the probability that a randomly selected CMSU student will be male?

We observe there are 5 males. Hence, the probability is 5/12

2. What is the probability that a randomly selected CMSU student will be female?

Since the remaining 7 are female, hence the probability is 7/12

3. Find the conditional probability of different majors among the male students in CMSU.

Out of the 5 males, one is undecided. Among the remaining, there are three different majors - Management, CIS and Others.

P (Management | Male) = 1/5

P (CIS | Male) = 1/5

P (Other | Male) = 2/5

P (Undecided | Male) = 1/5

4. Find the conditional probability of different majors among the female students of CMSU.

Among the females, everyone is decided and we see Economics/Finance instead of CIS.

P (Management | Female) = 1/7

P (Economics/Finance | Female) = 3/7

P (Other | Female) = 3/7

5. Find the conditional probability of intent to graduate, given that the student is a male.

P (GradIntention Yes | Male) = 3/5

P (GradIntention No | Male) = 1/5

P (GradIntention Undecided | Male) = 1/5

6. Find the conditional probability of intent to graduate, given that the student is a female.

P (GradIntention Yes | Female) = 3/7

P (GradIntention Undecided | Female) = 4/7

7. Find the conditional probability of employment status for the male students as well as for the female students.

There are three different status: Part-Time, Full-Time and Unemployed

P (Part-Time| Male) = 2/5

P (Full-Time | Male) = 2/5

P (Unemployed | Male) = 1/5

P (Part-Time| Female) = 2/7

P (Full-Time | Female) = 3/5

P (Unemployed | Female) = 2/5

8. Find the conditional probability of laptop preference among the male students as well as among the female students.

Among the males, everyone prefers a laptop and among females, one prefers tablet instead of laptop.

P (Laptop | Male) = 1

P (Laptop | Female) = 6/7

P (Tablet | Female) = 1/7