SOLUTION: I saw this problem: At Joe's Restaurant, one-fourth of the patrons are male and one-fifth of the patrons are from out of town. What proportion would you expect to be male and out

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Question 510774: I saw this problem:
At Joe's Restaurant, one-fourth of the patrons are male and one-fifth of the patrons are from out of town. What proportion would you expect to be male and out of town?
Someone answered it this problem like this:
For this kind of problem, you mulitply the two fractions. So 1/4 x 1/5 = 1/20. We would expect 1/20 of the patrons to be both male and from out of town.
Here is a way to visualize this.
In Town Out of Town Total
Male 4 1 5
Female 12 3 15
Total 16 4 20
Imagine that there are 20 people in the restaurant. Five are male (so 5/20 = 1/4) and 4 are from out of town (so 4/20 = 1/5). One way to show this is with the chart above. Only 1 person (1/20) is both male and from out of town.
My question is:
What is the reasoning behind the sentences below???? I don't understand that.
For this kind of problem, you mulitply the two fractions. So 1/4 x 1/5 = 1/20. We would expect 1/20 of the patrons to be both male and from out of town.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the key here may be "expect"

you know that 1/4 are male and 1/5 are from out of town

you would expect that the male patrons would have the same portion of out-of-towners as the female patrons

similarly, you would expect that the out-of-towners would have the same portion of males as the local patrons

either way you look at it, 1/5 of the males or 1/4 of the out-of-towners will give you the same "expected" result