SOLUTION: The probability that Nasim will study for her test is 3/10. The probability that she'll pass if she studies is 9/10. The probability that she'll pass if she doesn't study is 2/10.

Question 1174529: The probability that Nasim will study for her test is 3/10. The probability that she'll pass if she studies is 9/10. The probability that she'll pass if she doesn't study is 2/10. What is the probability that she has studied, given that she passes?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Studying and not studying are complementary events, so P(study)=3/10 means P(not study)=7/10. Then

P(study and pass) = (3/10)(9/10) = 27/100
P(not study and pass) = (7/10)(2/10) = 14/100

P(pass) = 27/100+14/100 = 41/100

P(pass|study) = (27/100)/(41/100) = 27/41

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