The answer is: 0.0362
The total number of Master's degree holders = 2848 (from the question)
In order to choose people 40 and above from this Master's degree holder subset,
You choose:
People 40-49 AND People 50 and over.
Number of people 40-49 = 475
Number of people 50 and over = 699
But we also need to take into consideration, the probability of picking a person 40-49 years old OR 50 and over
total Number of people 40 - 49 are 3518
The total Number of people 50 and above are 6518
Thus, we can write the probability as:
[tex]\begin{gathered} P(\text{choosing 40-49)=}\frac{475}{3518} \\ P(\text{choosing 50 and above)=}\frac{699}{6518} \\ P(choo\sin g\text{ Master's degre}e)=\frac{2848}{19076} \\ \\ \text{Thus, for choosing 40-49 AND Master's degre}e\colon \\ P(\text{choosing 40-49 AND Master's degr}ee)=\frac{475}{3518}\times\frac{2848}{19076}=0.0202 \\ \\ \text{For choosing 50 and above AND Master's degre}e\colon \\ P(\text{choosing 50 and above AND Master's degree)=}\frac{699}{6518}\times\frac{2848}{19076}=0.016 \\ \\ \text{Thus choosing Master's degree holder, 40 or over:} \\ P(\text{choosing 40-49 AND Master's degr}ee)+ \\ P(\text{choosing 50 and above AND Master's degree)} \\ =0.0202+0.016=0.0362 \end{gathered}[/tex]The final answer is: 0.0362
