8. The dean conducted a survey of students in which she asked ifthe student is p

Question

8. The dean conducted a survey of students in which she asked ifthe student is
part-time or full-time. Another question asked if the student votedor not in the
most recent election. The results follow:
Part-time Student Full-time Student Total
Voted 15 20 35
Did not vote 25 30 55
Total 40 50 90
Values in the table represent the number of respondents
If a student is selected at random (from this group of 90students), find the
probability
a. The student voted in the most recent election. (3)
b. The student voted in the most recent election and is a part-timestudent.
(3)
c. The student voted in the most recent election given the studentis part
time. (3)
d. Are the events “did not vote” and “full-timestudent” mutually exclusive?
Explain. (2)

5. The city council has three liberal members (one of whom is themayor) and two
conservative members. One member is selected at random to testifyin
Washington, D.C.
a. What is the probability the member is liberal? (3)
b. What is the probability the member is conservative? (3)
c. What is the probability the mayor is chosen? (3)

Explanation / Answer

8. The dean conducted a survey of students in which she askedif the student is
part-time or full-time. Another question asked if the student votedor not in the
most recent election. The results follow:
Part-time Student Full-time Student Total
Voted 15 20 35
Did not vote 25 30 55
Total 40 50 90
Values in the table represent the number of respondents
If a student is selected at random (from this group of 90students), find the
probability
a. The student voted in the most recent election. (3)

P[Voted] = 35/90 ˜ 0.3889

b. The student voted in the most recent election and is a part-timestudent.
(3)

P[Voted and Part-time] = 15/90 ˜ 0.1667

c. The student voted in the most recent election given the studentis part
time. (3)

P[Voted | Part-time] = #[Voted and Part-time] / #[Part-time] = 15/40 = 0.375

d. Are the events “did not vote” and “full-timestudent” mutually exclusive?
Explain. (2)

For events to be mutually exclusive then it means that it would notbe possible for BOTH to be true. Well, here it is certainlypossible that a student could be a full-time student who did notvote (there are 30 of them). So, these events are NOT mutuallyexcluisve.

5. The city council has three liberal members (one of whom is themayor) and two
conservative members. One member is selected at random to testifyin
Washington, D.C.

a. What is the probability the member is liberal? (3)

P[Liberal] = 3/5 = 0.6

b. What is the probability the member is conservative? (3)

P[Conservative] = 2/5 = 0.4

c. What is the probability the mayor is chosen? (3)

P[Mayor] = 1/5 = 0.2

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