Question

Sex	Industrial Engineering	Mechanical Engineering	Electrival Engineering	Civil Engineering	Total
Male	15	6	7	2	30
Female	10	4	3	6	23
Total	25	10	10	8	53

1.) Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument? (Problem A asked probability students are male which was 30/53=0.57 and Problem D asked probability student is industrial engineer given the student is male which ended up being 0.60)

2.) Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer.

3.) Find the probability that the randomly selected student is male or industrial engineering college major.

4.) Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer.

Answer 1

1) Let A be the event that student is a male

Probability of male , P(A) = 30/53 = 0.57

Let B be the event student is Industrial Engineer

P(A I B) = P(A B) / P(B) = (15/53) / (25/ 53) = 0.60

Since P(A) is not equal to P(A I B)

A and B are not independent events

Therefore sex and college major of students in this class are not independent

2) Two events A and B are mutually exclusive if

P(A B) = 0

Where A be the event that student is a male

and B be the event student is Industrial Engineer

P(A B) =15/53 is not equal to zero

A and B are not mutually exclusive

Again A be the event that student is a female

and B be the event student is Industrial Engineer

P(A B) =10/53 is not equal to zero

A and B are not mutually exclusive

3. Let A be the event that student is a male

P(A) = 30/53

Let B be the event student is Industrial Engineer

P(B) =25/53

P(A B) =15/53

P(A U B) = P(A) + P(B) -P(A B)

= 30/53 +25/53 - 15/53

= 0.75

Probability that a student is male or industrial engineering major = 0.75

4)

C be the event student is Industrial Engineer

D be the event student is Mechanical Engineer

P(C D) = 0

Thus C and D are mutually exclusive

Therefore , college major are mutually exclusive events