Question

assume that 70% of teenagers who go to take the written drivers license test have studied for the test. Of those who study for the test 95% pass; of the those who do not study for the test, 60% pass. what is the probability that a teenager who passes the written drivers license test did not study for the test?

Answer 1

$P = \frac{P(pass AND not study)}{P(pass AND study) + P(pass AND not study)} \\ \\ P = \frac{(.6)(.3)}{(.95)(.7) + (.6)(.3)} \\ \\ P = 0.213$