Question

Government data show that $8\%$ of adults are full-time college students and that $30\%$ of adults are age $55$ or older. Since $(0.08)(0.30)=0.024,$ can we conclude that about $2.4\%$ of adults are college students$55$ or older? Why or why not?

Short answer

Yes, because the events are independent events.

Step-by-step solution

Step 1. Given Information

$$\begin{gathered} P(Collegestudents)=8\%=0.08 \\ P(Age55orolder)=30\%=0.30 \\ P(CollegestudentsandAge55orolder)=2.4\%=0.024 \end{gathered}$$

Step 2. Concept Used

Two mutually exclusive events can never be independent since if one happens, the other is nearly surely going to happen as well.

Step 3. Calculation

$P(CollegestudentsandAge55orolder)=P(Collegestudents)\times P(Age55orolder)$

As a result, the above-mentioned criteria has been met. As a result, it's possible to deduce that $2.4$ percent of individuals are $55$ or older college students.