political ideologies preferences\n| |very lib...
political ideologies preferences\n| |very liberal| liberals| moderates| conservatives| very conservative| totals|\n|--|--|--|--|--|--|--|\n|teens (13 - 19)|24|30|16|8|2|\n|twenties (20 - 29)|19|55|21|4|1|\n|thirties (30 - 39)|8|34|61|29|14|\n|forties (40 - 49)|5|26|55|41|18|\n|fifties (50 - 59)|2|12|37|50|22|\n|sixties & up (60 - death)|0|7|40|67|24|\n|totals|\n\ngiven the table above, determine the probability of each event.\n1) p(selecting a liberal from all polled) = = %\n2) p(selecting a very conservative person from all polled) = = %\n3) p(selecting a person in their fifties from all polled) = = %\n4) p(selecting a moderate in their thirties from all polled) = = %\n5) p(selecting a very liberal in their teens from all polled) = = %\n6) p(selecting a very conservative from people in their sixties) = = %\n7) p(selecting a liberal from people in their twenties) = = %\n8) p(selecting a person in their forties from all moderates) = = %\n9) p(selecting a person in their sixties from all liberals) = = %
Answer
# Explanation:
## Step1: Calculate total number of people polled
First, find the sum of all values in the table.
$24 + 30+16 + 8+2+19+55+21+4+1+8+34+61+29+14+5+26+55+41+18+2+12+37+50+22+0+7+40+67+24$
$= (24 + 30+16 + 8+2)+(19+55+21+4+1)+(8+34+61+29+14)+(5+26+55+41+18)+(2+12+37+50+22)+(0+7+40+67+24)$
$= 80+100+146+145+123+138$
$= 732$
## Step2: Calculate probability of selecting a Liberal from all polled
Sum of Liberals: $30 + 55+34+26+12+7=164$
$P(\text{selecting a Liberal from all polled})=\frac{164}{732}\approx 0.224 = 22.4\%$
## Step3: Calculate probability of selecting a Very Conservative from all polled
Sum of Very Conservatives: $2 + 1+14+18+22+24 = 81$
$P(\text{selecting a Very Conservative from all polled})=\frac{81}{732}\approx 0.111 = 11.1\%$
## Step4: Calculate probability of selecting a person in their Fifties from all polled
Sum of values in Fifties row: $2+12 + 37+50+22=123$
$P(\text{selecting a person in their Fifties from all polled})=\frac{123}{732}\approx 0.168 = 16.8\%$
## Step5: Calculate probability of selecting a Moderate in their Thirties from all polled
Number of Moderates in Thirties is $61$
$P(\text{selecting a Moderate in their Thirties from all polled})=\frac{61}{732}\approx 0.083 = 8.3\%$
## Step6: Calculate probability of selecting a Very Liberal in their Teens from all polled
Number of Very Liberals in Teens is $24$
$P(\text{selecting a Very Liberal in their Teens from all polled})=\frac{24}{732}\approx 0.033 = 3.3\%$
## Step7: Calculate probability of selecting a Very Conservative from people in their Sixties
Sum of people in Sixties is $0 + 7+40+67+24=138$
Number of Very Conservatives in Sixties is $24$
$P(\text{selecting a Very Conservative from people in their Sixties})=\frac{24}{138}\approx 0.174 = 17.4\%$
## Step8: Calculate probability of selecting a Liberal from people in their Twenties
Sum of people in Twenties is $19+55+21+4+1 = 100$
Number of Liberals in Twenties is $55$
$P(\text{selecting a Liberal from people in their Twenties})=\frac{55}{100}=0.55 = 55\%$
## Step9: Calculate probability of selecting a person in their Forties from all Moderates
Sum of Moderates: $16+21+61+55+37+40 = 230$
Number of Moderates in Forties is $55$
$P(\text{selecting a person in their Forties from all Moderates})=\frac{55}{230}\approx 0.239 = 23.9\%$
## Step10: Calculate probability of selecting a person in their Sixties from all Liberals
Sum of Liberals is $164$
Number of Liberals in Sixties is $7$
$P(\text{selecting a person in their Sixties from all Liberals})=\frac{7}{164}\approx 0.043 = 4.3\%$
# Answer:
1. $\frac{164}{732}\approx 22.4\%$
2. $\frac{81}{732}\approx 11.1\%$
3. $\frac{123}{732}\approx 16.8\%$
4. $\frac{61}{732}\approx 8.3\%$
5. $\frac{24}{732}\approx 3.3\%$
6. $\frac{24}{138}\approx 17.4\%$
7. $\frac{55}{100}=55\%$
8. $\frac{55}{230}\approx 23.9\%$
9. $\frac{7}{164}\approx 4.3\%$