1. The probability that a randomly selected respondent voted for candidate A can be calculated by summing the total percentage of respondents who voted for candidate A across all age groups.
Probability = (0.65)(0.09) + (0.54)(0.07) + (0.51)(0.16) + (0.54)(0.16) + (0.47)(0.30) + (0.47)(0.22) = 0.4183
Therefore, the probability that a randomly selected respondent voted for candidate A is 41.83%.
2. To calculate the probability that a randomly selected respondent is among those who voted for candidate A and aged 40–49 years, we multiply the percentage of respondents who fall into that category by the percentage of those who voted for candidate A in that age group.
Probability = (0.54)(0.16) = 0.0864
Therefore, the probability that a randomly selected respondent is among those who voted for candidate A and aged 40–49 years is 8.64%.
3. To calculate the probability that a randomly selected respondent is among those who voted for candidate B or aged 25–29 years, we sum the probabilities of these two groups.
Probability = (0.43)(0.07) + (0.46)(0.16) + (0.09) = 0.1416
Therefore, the probability that a randomly selected respondent is among those who voted for candidate B or aged 25–29 years is 14.16%.
4. To calculate the expected number of voters who were 50–64 years old if 1,000 more voters were surveyed, we multiply the percentage of respondents in that age group of the total number of respondents.
Expected number = 0.30(1000) = 300
Therefore, the expected number of voters who were 50–64 years old would be 300 if 1,000 more voters were surveyed.
5. To calculate the expected number of voters who were 25–29 years old or who voted for candidate B if 1,000 more voters were surveyed, we sum the percentages for these two groups and multiply by 1,000.
Expected number = (0.07 + 0.43 + 0.46) * 1000 = 960
Therefore, the expected number of voters who were 25–29 years old or who voted for candidate B would be 960 if 1,000 more voters were surveyed.
6. To determine whether it would have been more likely to poll a 50–64-year-old candidate A supporter or a 30–39-year-old candidate B supporter if 1,000 more voters were surveyed, we compare the probabilities for the two groups.
For 50–64-year-old candidate A supporters: Probability = 0.47 * 0.30 = 0.141
For 30–39-year-old candidate B supporters: Probability = 0.51 * 0.16 = 0.0816
Therefore, it would have been more likely to poll a 50–64-year-old candidate A supporter if 1,000 more voters were surveyed, as the probability is higher for this group compared to 30–39-year-old candidate B supporters.
A news network published the results of an exit poll conducted during a presidential election. The survey reported 15,590 total respondents. Respondents are categorized according to age-groups. Table 4 reflects the percentage distribution of respondents and the percentage of respondents from each group who voted for candidate A or candidate B.
The entries in the first column mean that 65% of the respondents who were aged 18-24 years at that time voted for candidate A and 31% chose candidate B. This led to a 4% unreported response, which could either mean that they did not cast a vote for president or they did not want to share their votes.
Table 4. Exit Poll Survey Results
Age (in years)
18–24
9%
25–29
7%
30–39
16%
40–49
16%
50–64
30%
65 or older
22%
Voted for candidate A 65%
54%
51%
54%
47%
47%
Voted for candidate B 31%
43%
46%
44%
52%
52%
Use the results of the exit poll to answer the succeeding questions.
If a respondent is randomly selected from the database, what is the probability that that person is among those who voted for candidate A?
If a respondent is randomly selected from the database, what is the probability that that person is among those who voted for candidate A and aged 40–49 years?
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?
If 1,000 more voters were surveyed, what would have been the expected number of voters from this group who were 50–64 years?
If 1,000 more voters were surveyed, what would have been the expected number of voters from this group who were 25–29 years or who voted for candidate B?
If 1,000 more voters were surveyed, would it have been more likely to poll a 50–64-year-old candidate A supporter than a 30–39-year-old candidate B supporter? How can you tell?
1 answer