SOLUTION: The probabiity that George will study for the test is 4/10. The probability that he will pass given that he studies is 9/10. The probability that he passes given that he doesn't st

Algebra ->  Probability-and-statistics -> SOLUTION: The probabiity that George will study for the test is 4/10. The probability that he will pass given that he studies is 9/10. The probability that he passes given that he doesn't st      Log On


   

Question 355032: The probabiity that George will study for the test is 4/10. The probability that he will pass given that he studies is 9/10. The probability that he passes given that he doesn't study is 3/10. What is the probability that he has studied given that he passes the test?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P(study) = 0.4
P(pass|study) = 0.9
P(pass|not study) = 0.3
P(study|pass) = ???
From the formula for conditional probability,
P(study|pass) = P(study AND pass)/P(pass),
=P(study AND pass)/[P(study AND pass) + P(not study AND pass)]
=P(pass|study)*P(study)/[P(pass|study)*P(study) + P(pass|not study)*P(not study)]
=0.9%2A0.4%2F%280.9%2A0.4%2B0.3%2A0.6%29
=0.36%2F0.54=2%2F3
Therefore the probability that he has studied given that he passes the test is 2/3.