To solve this problem, we need to determine the probability that a randomly chosen resident who has a master's degree is under age 40 (i.e., in the age groups 20-29 or 30-39). We'll follow these steps:
1. Identify the relevant data:
- For the age group 20-29 with a master's degree: 643 residents
- For the age group 30-39 with a master's degree: 984 residents
- For the age group 40-49 with a master's degree: 499 residents
- For the age group 50 and over with a master's degree: 117 residents
2. Calculate the total number of residents with a master's degree:
[tex]\[
\text{Total residents with a master's degree} = 643 + 984 + 499 + 117 = 2243
\][/tex]
3. Calculate the number of residents with a master's degree who are under age 40:
- This includes the residents in the age groups 20-29 and 30-39.
[tex]\[
\text{Residents under age 40 with a master's degree} = 643 + 984 = 1627
\][/tex]
4. Calculate the probability:
- The probability [tex]\( P \)[/tex] is calculated by dividing the number of residents with a master's degree who are under age 40 by the total number of residents with a master's degree.
[tex]\[
P(\text{under 40 | master's degree}) = \frac{\text{Residents under age 40 with a master's degree}}{\text{Total residents with a master's degree}} = \frac{1627}{2243}
\][/tex]
5. Simplify and round this probability to the nearest thousandth:
[tex]\[
\frac{1627}{2243} \approx 0.726
\][/tex]
Therefore, the probability that a randomly chosen resident who has a master's degree is under age 40 is approximately 0.726, rounded to the nearest thousandth.
