Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students. You overhear a classmate say he got into the college he wanted. What is the probability he didn't take an SAT prep course?

What steps would I take to solve this problem?

Answer: The probability he didn't take an SAT prep course = 0.985

Step-by-step explanation:

Let us first assume that he took SAT prep.

Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college. That is,

30 / 100 of 5 = 0.3 * 5 = 1.5

The probability he did take an SAT prep course and got admission into the college of first choice will be

P (prep) = 1.5 / 100 = 0.015

The probability he didn't take an SAT prep course will be:

P (not prep) = 1 - P (prep)

P (not prep) = 1 - 0.015

P (not prep) = 0.985