Question

One hundred students were asked what kind of music they like to listen to. The results are in the table below.

	Classical	Rock	Jazz	Folk
Female	2	13	15	2
Male	7	14	3	4

If one student is selected randomly, find the following probabilities:
a) Student is a female

b) Student likes classical music

c) Student is a female and likes classical music

d) Student likes classical music given she is female

e) Are the events “female” and “likes classical music” mutually exclusive?

Select one:

a. No; because there's are females that like classical music

b. Yes; because there's are females that like classical music

f) Are they independent?

Select one:

a. Not Independent because the probability of "Classical" does not depend on "Female"

b. Not Independent because the probability of "Classical" depends on "Female"

c. Independent because the probability of "Classical" does not depend on "Female"

d. Independent because the probability of "Classical" depends on "Female"

Answer 1

	Classical	Rock	Jazz	Folk	Total
Female	3	14	16	2	35
Male	8	15	4	5	32
Total	11	29	20	7	67

a)

Probability that student is a female = Number of female students / Total students = 35 / 67 = 0.5224

b)

Probability that Student likes classical music = Number of students who like classical music / Total students =

= 11 / 67 = 0.1642

c)

Probability that Student is a female and likes classical music =

= Number of students who are female and like classical music / Total students

= 3 / 67 = 0.0448

d)

Probability that Student likes classical music given she is female = P( Student likes classical music | Student is female) =

= Probability that Student is a female and likes classical music / Probability that student is female

We already calculated :

Probability that Student is a female and likes classical music = 0.0448

Probability that student is female = 0.5224

So,

Probability that Student likes classical music given she is female = 0.0448 / 0.5224 = 0.0857

e)

Correct option : a. No; because there's are females that like classical music

Reason : Two events are mutually exclusive or disjoint if they cannot both occur at the same time. Since, there are Students that can be female and at the same time like classical music , therefore, events “female” and “likes classical music” are not mutually exclusive.

f)

Two event A and B can be independent if :

P(A | B ) = P(A)

Events “female” and “likes classical music” will be independent if :

P( Student likes classical music | Student is female) = P(Student likes classical music)

We already calculated:

P( Student likes classical music | Student is female) = 0.0857

P(Student likes classical music) = 0.1642

Since,

P( Student likes classical music | Student is female) P(Student likes classical music)

Hence, “female” and “likes classical music” are not independent.

Correct option : b. Not Independent because the probability of "Classical" depends on "Female"