- 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 B or aged 25-29 years?
To calculate the probability that the person voted for candidate B or is aged 25-29 years, we need to add the individual probabilities of voting for candidate B and being aged 25-29 years, and then subtract the probability of being both.
P(voted for B or aged 25-29) = P(voted for B) + P(aged 25-29) - P(voted for B and aged 25-29)
P(voted for B) = P(18-24 and voted for B) + P(25-29 and voted for B) + P(30-39 and voted for B) + P(40-49 and voted for B) + P(50-64 and voted for B) + P(65+ and voted for B)
P(voted for B) = 0 + 0.43 + 0.46 + 0.44 + 0.52 + 0.52
P(voted for B) = 2.37
P(aged 25-29) = 0.54
P(voted for B and aged 25-29) = P(25-29 and voted for B)
P(voted for B and aged 25-29) = 0.43
P(voted for B or aged 25-29) = 2.37 + 0.54 - 0.43
P(voted for B or aged 25-29) = 2.91
Therefore, the probability that the person randomly selected from the database voted for candidate B or is aged 25-29 years is 0.91 or 91%.