probability question. Problem is in comment. Thank you.

Question

how do i know if it is a probability theory or discrete probability distribution and how do I solve, what formula do I use?

 

here is my problem:

 

A country club is trying to understand the demographics of its members. The club finds that 70% of its members live within 10 miles of the club. Of the members that live within 10 miles of the club, 80% of them spend at least $200 per month at the club. Finally, only 30% of the members who live outside of 10 miles from the club spend over $200 per month at the club. What is the probability that a randomly chosen member lives outside 10 miles from the club?

Answer 1

If you look at that last sentence, it says it all. What is the probability that a randomly chosen member lives outside 10 miles from the club? First I would ask, who lives inside and outside 10 miles?

 

Earlier, the problem states that 70% of its members live within 10 miles. That would imply, 30% of its members live outside 10 miles of the club. You don't have to worry about how much the members that live closer to the club spend, because that is not what the question is asking.

 

100%-70% (people within 10 miles) = 30% (people that live outside the club) probability. 

                                                     = .3 if the question was asking for the proportion of people.