Question

1. It is known from past experience that for students who studied AMA1110 for at least 100 hours, their chance of passing the exam is 0.95, while for those who studied AMA1110 for less than 100 hours, their chance of passing the exam is 0.1. It is also known that the passing rate is 90%. If a student is randomly chosen and is found to have passed, what is the probability that he/she has studied for less than 100 hours? [8 marks]

Answer 1

Giveu P( Pass x>100) = 0-95 P (Pass | x <100) = 0 10 P(Pass) wherme is is the numben of hours studied AMA II IO. To find P(x<100 | Pass) Px (100 ( Pass) = P (Pass|x C100) .P (x <1o0) P(Pass) O'10 X0:0S88 = 0 0065 0.90 passed, proba bility that than If a studeut is touad to have he/she hour s = 0.0065 studied for 100 less P (x <100) = ? Note. P(fa ss) = P(Pass |x>10) . P(x>10) +P(Race)X cre).P(xcnd = 0'a5 1-P(X <io+ o10. P(x (100) 0.90 0.90 = 0 95 - 0:95X P (x <100)+ 010 P(X Goo)