a) what percent of these tampa, fl voters ide...
a) what percent of these tampa, fl voters identify themselves as conservatives? p(conservative) = 38.64 %\nb) what percent of these tampa, fl voters are in favor of the citizenship option? p(citizenship) = 34.66 %\nc) what percent of these tampa, fl voters identify themselves as conservative and are in favor of the citizenship option? p(conservative and citizenship) = 4.37 %\nd) what percent of these tampa, fl voters identify themselves as conservative or are in favor of the citizenship option? p(conservative or citizenship) = 68.93 %\ne) what percent of these tampa, fl voters are in favor of the citizenship option given they identify themselves as conservatives? p(citizenship | conservative) = 11.31 %\nf) what percent of these tampa, fl voters are in favor of the citizenship option given they identify themselves as moderates? p(citizenship | moderate) = 29.23 %\ng) what percent of these tampa, fl voters are in favor of the citizenship option given they identify themselves as liberals? p(citizenship | liberal) =\n(i) apply for citizenship 45 102 210 357\n(ii) guest worker 131 106 38 275\n(iii) leave the country 167 101 22 290\n(iv) not sure 55 40 13 108\ntotal 398 349 283 1030
Answer
# Explanation:
## Step1: Calculate total number of voters
The total number of voters is given as 1030.
## Step2: Calculate P(Conservative)
The number of conservative voters is 398. So $P(\text{Conservative})=\frac{398}{1030}\times100\approx 38.64\%$.
## Step3: Calculate P(Citizenship)
The number of voters in favor of citizenship option is 357. So $P(\text{Citizenship})=\frac{357}{1030}\times100\approx 34.66\%$.
## Step4: Calculate P(Conservative and Citizenship)
The number of voters who are conservative and in - favor of citizenship is 45. So $P(\text{Conservative and Citizenship})=\frac{45}{1030}\times100\approx 4.37\%$.
## Step5: Calculate P(Conservative or Citizenship)
Using the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of being conservative and $B$ is the event of being in favor of citizenship. So $P(\text{Conservative or Citizenship})=\frac{398 + 357- 45}{1030}\times100=\frac{710}{1030}\times100\approx 68.93\%$.
## Step6: Calculate P(Citizenship | Conservative)
Using the formula $P(B|A)=\frac{P(A\cap B)}{P(A)}$, where $A$ is the event of being conservative and $B$ is the event of being in favor of citizenship. $P(A\cap B)=\frac{45}{1030}$ and $P(A)=\frac{398}{1030}$, so $P(\text{Citizenship | Conservative})=\frac{45}{398}\times100\approx 11.31\%$.
## Step7: Calculate P(Citizenship | Moderate)
First, find the number of moderate voters. Assume we can calculate it from the table (not shown in full here but we know the total and other groups). Let's say the number of moderate voters is $n_{m}$. And the number of moderate voters in favor of citizenship is $n_{mc}$. Then $P(\text{Citizenship | Moderate})=\frac{n_{mc}}{n_{m}}\times100$. If we assume from the data that the number of moderate voters is 349 and the number of moderate voters in favor of citizenship is 102, then $P(\text{Citizenship | Moderate})=\frac{102}{349}\times100\approx 29.23\%$.
## Step8: Calculate P(Citizenship | Liberal)
Let the number of liberal voters be $n_{l}$ and the number of liberal voters in favor of citizenship be $n_{lc}$. Assume from the data that the number of liberal voters is 283 and the number of liberal voters in favor of citizenship is 210. Then $P(\text{Citizenship | Liberal})=\frac{210}{283}\times100\approx 74.20\%$.
# Answer:
a) $38.64\%$
b) $34.66\%$
c) $4.37\%$
d) $68.93\%$
e) $11.31\%$
f) $29.23\%$
g) $74.20\%$