A calculus class is composed of 35 men and 45 women...

Question

A calculus class is composed of 35 men and 45 women. There are 20 business majors, 30 biology, 10 computer science and 20 math majors. No person has a double major. If a single student is chosen from the class, what is the probability of the event that the student is a computer science OR math major?

Answer 1

If you are randomly selecting a student from the class, let the events A and B be such that A =  “Student is a computer science major” and B = “Student is a math major”.

In this case,

P(A) = (# computer science majors)/(Total students in class) = 10/80

P(B) = (# math majors)/(Total students in class) = 20/80

We can further note that the events A and B are disjoint - it’s impossible for a student to be both a computer science major and a math major because no person has a double major.

Therefore, by the addition rule for disjoint events,

P(A or B) = P(A) + P(B) = 10/80 + 20/80 = 30/80 = 0.375

There is a 37.5 % chance that a randomly selected student is a computer science or math major.

Answer 2

35 + 45 = 80 people

P1 = prob(comp sci) = 10 / 80 = 1 / 8

P2 = prob(math) = 20 / 80 = 2 / 8

P = P1 + P2 = 1 / 8 + 2 / 8 = 3 / 8