Question 1209863: A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
better same worse
Republican 38 104 44
Democrat 12 87 137
none 21 90 118
Express your answers as a decimal and round to the nearest 0.001 (in other words, type 0.123, not 12.3% or 0.123456).
If we randomly select one of the adults who participated in this study, compute:
P(Republican) =
P(better) =
P(better|Republican) =
P(Republican|better) =
P(Republican and better) =
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the probabilities based on the provided table:
**1. Calculate the Total Number of Respondents:**
* Total = 38 + 104 + 44 + 12 + 87 + 137 + 21 + 90 + 118 = 651
**2. Calculate the Required Probabilities:**
* **P(Republican):**
* Total Republicans = 38 + 104 + 44 = 186
* P(Republican) = 186 / 651 ≈ 0.286
* **P(better):**
* Total "better" responses = 38 + 12 + 21 = 71
* P(better) = 71 / 651 ≈ 0.109
* **P(better|Republican):**
* This is the probability of "better" given that the person is a Republican.
* P(better|Republican) = (Number of Republicans who said "better") / (Total Republicans)
* P(better|Republican) = 38 / 186 ≈ 0.204
* **P(Republican|better):**
* This is the probability of being a Republican given that the person said "better".
* P(Republican|better) = (Number of Republicans who said "better") / (Total "better" responses)
* P(Republican|better) = 38 / 71 ≈ 0.535
* **P(Republican and better):**
* This is the probability of being a Republican and saying "better".
* P(Republican and better) = (Number of Republicans who said "better") / (Total respondents)
* P(Republican and better) = 38 / 651 ≈ 0.058
**Results:**
* P(Republican) ≈ 0.286
* P(better) ≈ 0.109
* P(better|Republican) ≈ 0.204
* P(Republican|better) ≈ 0.535
* P(Republican and better) ≈ 0.058
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