Question

A volunteer for the Drug & Alcohol Education Center was investigating the attitudes of XYZ students towards binge drinking on campus. A simple random sample of 730 students from all four grade levels was taken. Each student was given the statement “Binge drinking of LMU students has become too frequent and dangerous,” and asked whether they strongly agreed, agreed, had no opinion, disagreed, or strongly disagreed. The following contingency table summarizes the results.

Complete the contingency table in order to answer the questions on next page.

Grade	Strongly Agree	Agree	No opinion	Disagree	Strongly disagree	Totals
Freshman		37	11	92	49
Sophomore	35	28		59	28	175
Junior	36	32	39	43		190
Senior	48	38	22		14	153
Totals	142		97	225	131	730

1. What is the probability of those students who have no opinion?
2. What is the interpretation of this probability?
3. Compute the conditional probability that a student disagreed with the statement given they were a junior.
4. What is the interpretation of this conditional probability?
5. What is the conditional probability that a student was a sophomore given they strongly agreed?

Answer 1

Solution(a)

P(No opinion) = Total No. of students with No opinion/ Total no. of Student. = 97/730 = 0.1329
Solution(b)
There is 13.29% probability that student have no opinion
Solution(c)
P(Student Disagreed | Student were Junior) = P(Student Disagreed and Student Were Junior)/P(Student Were Junior) = (43/730)/(190/730) = 43/190 = 0.2263
Solution(d)
So there is 22.63% probability that a student disagreed with the statement given they were a junior.
Solution(e)
P(Student was sophomore | Strongly agreed) = P(Student was sophomore and Strongly Agreed) / P(Strongly Agreed) = (36/430)/ (142/430) = 0.2535