Question

In the current first-year class of a community college, all the students come from three local high schools. Schools I, II, and III supply respectively 40%, 50%, and 10% of the students. The failure rate of students is 4%, 2%, and 6%, respectively. Given that a student fails, what is the probability that he or she came from school I?

Answer 1

ANSWER::

Given,

40% of students come from School I. So, P(S1) =0.4

50% of students come from School II. So, P(S2) =0.5

10% of students come from School III. So, P(S3) =0.1

Failure rate of students are 4% 2% and 6% respectively.

Hence, probability that a student fails is [(0.04*0.4) + (0.02*0.5) + (0.06*0.1) ]= 0.032

We need to find the probability that the student comes from School I given that he or she failed

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