Probability of a Survey 
Among the participants in a survey,
  
  
*
  
*$30\%$ live in the suburbs
  
*$50\%$ are over $40$ years old
One participant is selected at random. The sharpest bound that can be justified based on the information given on the chance that the participant lives in the suburbs and is over $40$ years old is?

How would you approach such a probability? 
(Participants lives in Suburbs and Over 40 Years old)=Multiple Rule; 
$P($Participant Suburbs$) \cdot P($Over 40 Years Old$) =
(0.30 \cdot 0.50)=0.15=$ at the most $15\%$?

It is conceivable  that nobody in the suburbs is over $40$. It is conceivable that everybody in the suburbs is over $40$.  So the sharpest certain estimate is that the percentage in the suburbs and over $40$  is between $0$ and $30$ percent. 
Remark: The truth for sure lies between $0$ and $30$. Multiplying $0.3$ by $0.5$ as in your proposal assumes independence of the events "lives in the suburbs" and "is over $40$." These events are undoubtedly not independent.
