Answer :
To solve the problem of finding the probability that a randomly chosen voter from the survey will be aged between 39 and 49 and registered as a Republican, we can follow these steps:
1. Identify the total number of voters: The total number of voters surveyed is given in the table, listed under the "Total" column.
[tex]\[ \text{Total number of voters} = 3228 \][/tex]
2. Identify the number of voters who are between 39 and 49 and registered as Republicans: From the table, the number of Republicans aged between 39 and 49 is specifically mentioned.
[tex]\[ \text{Number of Republicans aged 39-49} = 250 \][/tex]
3. Calculate the probability: The probability [tex]\( P \)[/tex] that a randomly chosen voter is aged between 39 and 49 and registered as a Republican is calculated by dividing the number of Republicans aged 39-49 by the total number of voters.
[tex]\[ P = \frac{\text{Number of Republicans aged 39-49}}{\text{Total number of voters}} \][/tex]
[tex]\[ P = \frac{250}{3228} \][/tex]
4. Perform the division: Calculate the division to find the probability.
[tex]\[ P \approx 0.07744733581164807 \][/tex]
5. Round to the nearest hundredth: To obtain the final answer, round the obtained probability to the nearest hundredth.
[tex]\[ P \approx 0.08 \][/tex]
Thus, the probability that a randomly chosen voter from the survey will be between 39 and 49 years old and registered as a Republican is approximately 0.08.
1. Identify the total number of voters: The total number of voters surveyed is given in the table, listed under the "Total" column.
[tex]\[ \text{Total number of voters} = 3228 \][/tex]
2. Identify the number of voters who are between 39 and 49 and registered as Republicans: From the table, the number of Republicans aged between 39 and 49 is specifically mentioned.
[tex]\[ \text{Number of Republicans aged 39-49} = 250 \][/tex]
3. Calculate the probability: The probability [tex]\( P \)[/tex] that a randomly chosen voter is aged between 39 and 49 and registered as a Republican is calculated by dividing the number of Republicans aged 39-49 by the total number of voters.
[tex]\[ P = \frac{\text{Number of Republicans aged 39-49}}{\text{Total number of voters}} \][/tex]
[tex]\[ P = \frac{250}{3228} \][/tex]
4. Perform the division: Calculate the division to find the probability.
[tex]\[ P \approx 0.07744733581164807 \][/tex]
5. Round to the nearest hundredth: To obtain the final answer, round the obtained probability to the nearest hundredth.
[tex]\[ P \approx 0.08 \][/tex]
Thus, the probability that a randomly chosen voter from the survey will be between 39 and 49 years old and registered as a Republican is approximately 0.08.
