Answer to Question #166470 in Statistics and Probability for phemelo mongae

Question

 The probability that a student passes Probability is 0.8 if she studies for the exam and 0.3 if she does not study. If 60% of the class studied for the exam, and a student picked a random from the class has passed, what is the probability that she studied for the exam?

Answer 1

Events:

A - a student picked a random from the class has studied. P(A) = 0.6

$\lnot$A - a student picked a random from the class has not studied. P($\lnot$A) = 0.4

В - a student picked a random from the class has passed.

B|A - a student picked a random from the class has passed if she does study. P(B|A) = 0.8

B|$\lnot$A - a student picked a random from the class has passed if she does not study. P(B|$\lnot$A) = 0.3

A|B - a student picked a random from the class has studied if she does pass.

P(A|B) = P(B|A)*P(A)/P(B) = P(B|A)*P(A)/(P(A)*P(B|A)+P($\lnot$A)*P(B|$\lnot$A)) = 0.8*0.6/(0.6*0.8+0.4*0.3) = 0.8