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 high school student say he got into the college he wanted. What is the probability he didn't take an SAT prep course?

From the Statistics you have, you can see that taking a SAT prep course does not guarantee success. However, if you do not even enroll in a SAT prep course, there is little, if any, chance of success. Most college-bound students are wise to take the prep courses.

Sra

I will get my book out but perhaps a stats teacher can help before I get at it.

make a "tree" of possiblilites

start with two branches
A) took SAT prep test
B) did not take SAT prep test

mark each with a prob of .5

Split A) into two more braches
C) got in to first choice college, prob .3
D) did not get into first choice college, prob .7

Split B) into two similar branches
E) prob .2
F) prob .8
<<..You overhear a high school student say he got into the college he wanted. What is the probability he didn't take an SAT prep course..>
Sounds like BE which would have a prob of
(.5)(.2) = .1 or 10%

I assume that the entire sample took the SAT

Call total number of students t
.05 t took prep
.3*.05 t = .015 t = number who took prep and got in
.95 t did not take prep
.2*.95 t = .19 t = number who got in and did not take prep

So 19%

notice my possible outcomes are

AC - took the prep test and got in -- (.5)(.3) = .15
AD - took the prep test, did not get in -- (.5)(.7) = .35
BE - did not take prep test but still got in --- (.5)(.2) = .1
BF - did not take prep test, did not get in --- (.5)(.8) = .4

my 4 prob add up to 1, as they should

It said 5% not 50%

Damon is right, (time to get new reading glasses at the dollar store)

thanks for your help!!:)

the answer is 93% but i have no idea how to get there

93% is right, instead of making a tree with .5 for the first two branches. The branch for taking prep should be .05 since 5% of the people taking the SATs have taken a prep course, then the branch for people who haven't taken a prep course for the SATs should be .95