Suppose a class has 28 freshmen, 12 sophomores, 8 juniors, and 3 seniors in it. If 3 student names are drawn, what is the probability that they are freshmen?

Question

I want to know how to do this probability problem

Answer 1

28 + 12 + 8 +3 = 51 students in total.

Since there are 28 fm, the first pull is 28/51. I'm assuming that the names are kept pull out, so the next ones would be 27/50 and 26/49.

 

Multiplying it all together, it looks like:

28 * 27 * 26

---------------

51 * 50 * 49

 

19656 / 124950

Which becomes about 15.73%

 

If you want to keep it as a fraction probability, we can simplify terms a bit:

14 * 9 * 26
---------------
17 * 25 * 49

 

Which further reduces to:

2 * 9 * 26
---------------
17 * 25 * 7

 

That's all of the simplification we can do, so it becomes:

268/2975