3. Consider the results of a recent survey of 200 randomly selected Mason studen

Question

3. Consider the results of a recent survey of 200 randomly selected Mason students. StatePrefer Action Prefer Prefer Movies 40 20 Total Movies Romance Comedy Arkansas California Total 60 50 110 Movies 10 20 30 110 90 200 60 Identify the events (e.g., A: Arkansas), phrase each of the problems below using the events, set and probability notation (e.g, P(RIA)) a. What is the probability that a student prefers Action Movies? b. What is the probability that a student's home state is California? c. If the student's home state is Arkansas, what is the probability that the student prefers Romance Movies? If the student's home state is California, what is the probability that the student prefers Romance or Comedy movies? d. e. Is the type of movie preferred independent of the student's home state? Use a formula and data from the table to justify your answer

Explanation / Answer

S- sample space

n(S)=200

a.)

Let Ac be the event that student prefers action Movies .

answer: P(Ac)= n(Ac)/n(S) = 110/200= 11/20

b)

Let C be the event that students home state is california

answer: P(C) = n(C)/n(S) = 90/200 = 9/20

c)

Let A be the event that students home state is Arkansas

Let R be the event that student prefers romance movies

answer: P(R | A) i.e probability of student preferring romance given that his/her home state is Arkansas

=n(R and A)/n(A) i.e probability = ratio of number of students in (R and/intersection A) by number of students in A

=10/110 = 1/11

d)

Events are independant if the occurrence of one does not effect the occurrence/probability of another.

for e.g

1)

P(R | A) i.e probability of student preferring romance given that his/her home state is Arkansas

=n(R and A)/n(A) i.e probability = ratio of number of students in (R and/interscetion A) by number of students in A

=10/110 = 1/11

2)

P(R | C) i.e probability of student preferring romance given that his/her home state is California

=n(R and C)/n(C) i.e probability = ratio of number of students in (R and/intersection C) by number of students in C

=20/90 = 2/9

so from 1 and 2 since the probability of R changes with state ,it is clear that type of movie preferred is DEPENDANT of students's home state

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.