Part 2: Calculating Probabilities
Problem 2
Problem Statement
The local college had 578 new students register for courses this semester. Many of the students enrolled into one
or more courses from the humanities, science, business, or math departments as shown in the Venn Diagram
here.
Questions
1. Based on the current data, what department has the highest probability of “new student enrollment?”
Give your answers as a fraction in lowest terms.
a. What is the probability a new student enrolls into a humanities course?
b. What is the probability a new student enrolls into a science course?
c. What is the probability a new student enrolls into a math course?
d. What is the probability a new student enrolls into a business course?
e. Which of the four departments has the highest probability of “new student enrollment?”
Humanities Science
Business Math
18
22
15
9
27
37 40
22
31
47
18
76
50
6
2. Based on the current data, what is the probability a new student enrolled in a science course is also
enrolled in a math course? Give your answer as a fraction in lowest terms.
3. Based on the current data, what is the probability a new student enrolled in a science course is also
enrolled in a math and humanities course? Give your answer as a fraction in lowest terms.
4. Based on the current data, which department has the highest probability of students enrolled in one of
their courses only? Give your answer as a fraction in lowest terms.
a. What is the probability a new student enrolled in a math course is enrolled only in a math
course?
b. What is the probability a new student enrolled in a business course is enrolled only in a
business course?
c. What is the probability a new student enrolled in a science course is enrolled only in a science
course?
d. What is the probability a new student enrolled in a humanities course is enrolled only in a
humanities course?
e. Which department has the highest probability of students enrolled in one of their courses only?
5. If the current data is an accurate predictor of future new student enrollment, how many students should
the college expect to enroll into a course from all four departments if 900 new students enroll next
semester?
a. What is the probability a new student will enroll into a course from all four departments? Give
your answer as a fraction in lowest terms.
b. How many students should the college expect to enroll into a course from all four department if
900 new students enroll next semester? Give your answer as a whole number.