A Gallup poll conducted in 2012 asked people, “Do you think the United States be
ID: 3158566 • Letter: A
Question
A Gallup poll conducted in 2012 asked people, “Do you think the United States benefits from having a class of rich people?” In response, 80% of Republicans, 59% of Independents, and 52% of Democrats said Yes. Assume that any- one who did not answer Yes answered No. Suppose the number of Republicans polled was 400, the number of Democrats was 500, and the number of Independents was 100.
a. What is the probability that a person randomly selected is a Democrat given they said Yes?
b. What is the probability that a person randomly selected is a Republican given they said Yes.?
c. What is the probability that a person randomly selected said Yes given they are a Democrat?
d. What is the probability that a person randomly selected from the entire group is a Democrat AND said Yes?
Explanation / Answer
A Gallup poll conducted in 2012 asked people, “Do you think the United States benefits from having a class of rich people?” In response, 80% of Republicans, 59% of Independents, and 52% of Democrats said Yes. Assume that any- one who did not answer Yes answered No. Suppose the number of Republicans polled was 400, the number of Democrats was 500, and the number of Independents was 100.
We can make the following table.
Yes
No
Total
Republican
320
80
400
Independent
59
41
100
Democrats
260
240
500
Total
639
361
1000
P=260/639 =0.4069
P=320/639 =0.5008
P=260/500 =0.520
d. What is the probability that a person randomly selected from the entire group is a Democrat AND said Yes?
P=260/1000 =0.260
Yes
No
Total
Republican
320
80
400
Independent
59
41
100
Democrats
260
240
500
Total
639
361
1000
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