Question

The following table represents the highest educational attainment of all adultresidents in a certain town. If a resident who has a master's degree is chosen atrandom, what is the probability that they are aged 40 or over? Round your answer tothe nearest thousandth.

Answer 1

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:

`\begin{gathered} P(\text{choosing 40-49)=}(475)/(3518) \\ P(\text{choosing 50 and above)=}(699)/(6518) \\ P(choo\sin g\text{ Master's degre}e)=(2848)/(19076) \\ \\ \text{Thus, for choosing 40-49 AND Master's degre}e\colon \\ P(\text{choosing 40-49 AND Master's degr}ee)=(475)/(3518)*(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)=}(699)/(6518)*(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}`

The final answer is: 0.0362