A company with good finance assessment has very high probability (0.95) of good

Question

A company with good finance assessment has very high probability (0.95) of good finance situation in the coming year. In a recent survey in a Statistics class, it was determined that only 60% of the students attend class on Thursday. From past data it was noted that 98% of those who went to class on Thursday pass the course, while only 20% of those who did not go to class on Thursday passed the course. (a) What percentage of students is expected to pass the course? (b) Given that a student passes the course, what is the probability that he/she attended classes on Thursday [solution:] A1: the students attend class on Thursday A2: the students do not attend class on Thursday

Explanation / Answer

A1: students attend class on Thursday => P(A1)=0.6

A2: students dont attend class on thursday=>P(A2)=0.4 i.e 1-0.6

P(pass | A1)=0.98

P(pass | A2)=0.2

a) Thus, P(pass)=P(pass|A1)*P(A1)+P(pass|A2)*P(A2)= 0.98*0.6+0.2*0.4=0.668

b) P(A1|pass)=P(pass|A1)*P(A1)/P(pass)=0.98*0.6/0.668=0.88024

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