Question

Currently Enrolled Course

Gender		Engnr 10	Math 100	Physics 101	Total
	Female	40	20	20	80
	Male	120	60	60	240
	Total	160	80	80	320

a. Selecting a student at random, what is the probability that the student is enrolled in Physics 101?

b. If we randomly select a male student, what is the probability that he is enrolled in Physics 101?

Using percentages (probabilities) from part a and part b, Is enrolling in Physics 101 independent of a student’s gender? Explain.

Answer 1

a) Total number of students=320

Total number of students enrolled in Physics 101=80

So P(a student selected in enrolled in Physics 101)=80/320=0.25

b) Total number of male students=240

Total number of male students enrolled in Physics 101=60

P(a selected male student is enrolled in physics 101)=60/240=0.25

c) As both the probabilities are same that is equal to 0.25 we can say that enrolling in Physics 101 is independent of students gender. A statistical reason for this is as follows:

Suppose A and B are two events and P(A given B) and P(A given B compliment) is same then we can say that A and B are independent.

So in this case A is that student has enrolled in Physics 101 and B is that the student is a male.

And as calculated the probabilities above we can say events are independent.