Probability and Percent Problem (Please Help ;)

Question

At a certain college, 70% of the students are 21 years of age or younger. 50% of students are female, and 30% of all students are both female and 21 years of age or younger. If one student is selected at random, find the probability that this student is male and over 21 years of age.

 

 

Thank you!

Answer 1

Let X represent the total population at the college.

 

.70x = total number of students 21 years or younger.

.50x = total number of students who are female

.30x = total number of students who are both female and 21 years of age or younger.

 

So, we know that the probability of 2 things happening is the probability of one multiplied by the probability of the other. In this case, those two things are that a student is male and over 21 years of age.

 

The probability that a student is male is equal to 50%. We know this because 100%-50% (the probability that a student is female) = 50%.  Using the same logic, we know that there is a 30% chance that any one student is over the age of 21.

 

Thus, .50 x .30 = .15.  There is a 15% chance that any one student chosen at random is both male and over the age of 21.