Question

Probability: Apply

Try This
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?

I'm so confused and can't focus pls explain simply, I'm 8 assignments behind on math and I have 2 says left of school idk how I'm gonna finish it bc it's SOOO hard

Answer 1

[AI-generated answer — Bot GPT 3.5]

Don't worry, I'll help you understand these questions step by step.

1. The probability that a randomly selected respondent voted for candidate A can be found by adding up the percentages of each age group who voted for candidate A. The sum of these percentages is 65% + 54% + 51% + 54% + 47% + 47% = 318%. However, since the total percentage should add up to 100%, we need to divide this by 100 to get the probability: 318% / 100% = 3.18 or 3.18%.

2. The probability that a respondent who is among those who voted for candidate A and aged 40-49 years can be calculated by multiplying the percentage of people aged 40-49 who voted for candidate A by the percentage of all respondents who are in that age group. This would be 54% x 16% = 8.64%.

3. To find the probability that a respondent is among those who voted for candidate B or aged 25-29 years, you need to add the percentage of people aged 25-29 who voted for candidate B to the percentage of all respondents who are in that age group. This would be 43% + 7% = 50%.

4. To find the expected number of voters from the group who are 50-64 years old if 1,000 more voters were surveyed, you can multiply the percentage of respondents who are 50-64 years old (30%) by the new total number of respondents (15,590 + 1,000 = 16,590). This would be 30% of 16,590, which is 4,977.

5. To find the expected number of voters who are 25-29 years old or who voted for candidate B if 1,000 more voters were surveyed, you can add the percentage of respondents who are 25-29 years old (7%) to the percentage of respondents who voted for candidate B (31%). Then, multiply the sum by the new total number of respondents (16,590). This would be (7% + 31%) of 16,590.

6. To determine whether it would have been more likely to poll a 50-64-year-old candidate A supporter than a 30-39-year-old candidate B supporter if 1,000 more voters were surveyed, you can compare the probabilities calculated in questions 4 and 5. The group with the higher probability would be more likely to be polled.

Answer 2

Are you sure?

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion in my previous response. Let's break it down further:

1. The probability that a randomly selected respondent voted for candidate A is calculated by adding up the percentage of respondents in each age group who voted for candidate A. This would be 65% of 9% (age 18-24) + 54% of 7% (age 25-29) + 51% of 16% (age 30-39) + 54% of 16% (age 40-49) + 47% of 30% (age 50-64) + 47% of 22% (age 65+). Add these up, and then divide by the total percentage of respondents (100%) to get the probability.

2. The probability that a respondent is both aged 40-49 years and voted for candidate A is achieved by multiplying the percentage of respondents aged 40-49 who voted for candidate A by the percentage of all respondents who are in that age group.

3. The probability that a respondent is either aged 25-29 years or voted for candidate B is calculated by adding the percentage of respondents aged 25-29 years to the percentage of respondents who voted for candidate B.

4. To find the expected number of voters aged 50-64 years if 1,000 more voters were surveyed, you multiply the percentage of respondents who are 50-64 years old by the new total number of respondents.

5. To find the expected number of voters who are aged 25-29 years or who voted for candidate B if 1,000 more voters were surveyed, you add the percentage of respondents aged 25-29 and the percentage of voters who chose candidate B and then multiply by the new total number of respondents.

6. To determine if it would have been more likely to survey a candidate A supporter aged 50-64 or a candidate B supporter aged 30-39 if 1,000 more voters were surveyed, you compare the probabilities calculated in questions 2 and 3 to see which is higher.

I hope this helps clarify things for you. Let me know if you need further explanation.

Answer 4

UPDATE: It's 1 hour later and I did the assignment now I need to do 7 more in 2 hours and they're pretty much the same😭

But we can get through it together💪

Answer 5

[AI-generated answer — Bot GPT 3.5]

That's the spirit! You can do it! If you need any help or have any questions while working on the remaining assignments, feel free to ask. We'll tackle them one by one and get through them together! Keep up the positive attitude, and you'll get those assignments done in no time. You've got this!💪🌟

Answer 6

It's ok Ik it's hard but you can do it

Answer 7

[AI-generated answer — Bot GPT 3.5]

Thank you for your encouragement! If you need help or support during the assignment, feel free to reach out. Remember, taking breaks and asking for help when needed can make things easier. You've got this, and I believe in you! Keep up the good work! 💪🌟 Let's tackle those assignments together!