For ages 18 to 24, the percentage who voted for candidate A is 65%
- For ages 25 to 29, the percentage who voted for candidate A is 54%
- For ages 30 to 39, the percentage who voted for candidate A is 30%
- For ages 40 to 49, the percentage who voted for candidate A is 16%
- For ages 50 to 64, the percentage who voted for candidate A is 30%
- For ages 65 or older, the percentage who voted for candidate A is 22%
For ages 18 to 24, the percentage who voted for candidate B is 31%
- For ages 25 to 29, the percentage who voted for candidate B is 43%
- For ages 30 to 39, the percentage who voted for candidate B is 46%
- For ages 40 to 49, the percentage who voted for candidate B is 44%
- For ages 50 to 64, the percentage who voted for candidate B is 52%
- For ages 65 or older, the percentage who voted for candidate B is 52%
if a respondent is randomly selected from the database, what is the probability that that person is among those who voted for candidate A?
To calculate the probability that a randomly selected respondent voted for candidate A, we need to consider the total number of respondents in each age group and the percentage of people who voted for candidate A in that group.
Let's assume there are 100 respondents in each age group for simplicity.
For ages 18 to 24:
Number of people who voted for candidate A = 65
Total number of respondents = 100
Probability = 65/100 = 0.65
For ages 25 to 29:
Number of people who voted for candidate A = 54
Total number of respondents = 100
Probability = 54/100 = 0.54
For ages 30 to 39:
Number of people who voted for candidate A = 30
Total number of respondents = 100
Probability = 30/100 = 0.3
For ages 40 to 49:
Number of people who voted for candidate A = 16
Total number of respondents = 100
Probability = 16/100 = 0.16
For ages 50 to 64:
Number of people who voted for candidate A = 30
Total number of respondents = 100
Probability = 30/100 = 0.3
For ages 65 or older:
Number of people who voted for candidate A = 22
Total number of respondents = 100
Probability = 22/100 = 0.22
To find the overall probability that a randomly selected respondent voted for candidate A, we need to calculate the weighted average of all age groups based on the total number of respondents in each group.
Weighted average probability = (65x100 + 54x100 + 30x100 + 16x100 + 30x100 + 22x100) / (100 + 100 + 100 + 100 + 100 + 100)
= (6500 + 5400 + 3000 + 1600 + 3000 + 2200) / 600
= 21700 / 600
= 36.17%
Therefore, the probability that a randomly selected person voted for candidate A is approximately 36.17%.