In the graduating class of a certain college, 48% of the students are male and 52% are female

In the graduating class of a certain college, 48% of the students are male and 52% are female. In this class 40% of the male and 20% of the female students are 25years old or older. If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old??
A) 0.90
B) 0.70
C) 0.45
D) 0.30
E) 0.25 


 




This is really just a weighted average. We have two groups, men and women, and men have an 'average' of 40%, while women have an 'average' of 20%. The groups are almost equal in size, so when we combine them, the 'average' must be almost exactly 30%. So roughly 30% of all people are twenty-five years old or older, and roughly 70% are thus less than twenty-five, so the answer should be B.
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Whenever we have groups (in this case, male and female) that are being divided into smaller groups (in this case, those 25 and older and those less than 25), we can use a group grid to organize the data. Here's what the grid looks like:

_______________M______F_______Total

older:

younger:

total:

In the grid above, every row has to add up to the total, as does every column. Looking at the top row, older males + older females = total older. Looking at the left-most column, older males + younger males = total males.



Now let's fill in the data step by step. Let's plug in 100 for the total number of students:

_______________M______F_______Total

older:

younger:

total:__________________________100



48% males, 52% females. Since we're looking for an approximation, let's say that 50% are males and 50% are females:

_______________M______F_______Total

older:

younger:

total:__________50_____50________100



40% of the males and 20% of the females are 25 and older:

_______________M______F_______Total

older:__________20_____10_______

younger:

total:__________50_____50________100



Now we can complete the grid:

_______________M______F_______Total

older:__________20_____10________30

younger:_______30_____40________70

total:__________50_____50________100


Notice that everything adds up horizontally and vertically. Neat!

So P(younger) = 70/100 = .7

The correct answer is B.