SOLUTION: a teacher has found that the probability that a student studies for a test is .6, the probability that a student gets a good grade on a test is .7 and the probability that a studen

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Question 464667: a teacher has found that the probability that a student studies for a test is .6, the probability that a student gets a good grade on a test is .7 and the probability that a student gets a good grade on a test is 07 and the probability that both occur is .52.
1. Are these events independent?
2. Given that the student studies, find the probability that the student gets a good grade.
3. Gicen that the student gets a good grade, find the probability that the student studies.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1) These events are not independent, because P%28studies++AND+good+grades%29%3C+%3EP%28studies%29+%2A+P%28good+grades%29.
2) P(good grades| studies) = P(studies AND good grades)/P(studies) = 0.52/0.6 = 13/15.
3) P(studies | good grades) = P(studies AND good grades)/P(good grades) = 0.52/0.7 = 26/35.