The enrolment records of a community college show that 40% offirst years student

Question

The enrolment records of a community college show that 40% offirst years students live in one of the college dormitories.Records also show that the graduation rate of the first yearstudents at this college is 75%. Assuming that these two factorsare independent of each other, what is the proability that arandomly selected first year student a.) lives in a dormintory and will graduate from thecollegre b.) does not live in a dormitory but will graduate from thecollege c.) does not live in a dormintory and will not graduate fromthe college The enrolment records of a community college show that 40% offirst years students live in one of the college dormitories.Records also show that the graduation rate of the first yearstudents at this college is 75%. Assuming that these two factorsare independent of each other, what is the proability that arandomly selected first year student a.) lives in a dormintory and will graduate from thecollegre b.) does not live in a dormitory but will graduate from thecollege c.) does not live in a dormintory and will not graduate fromthe college

Explanation / Answer

1) A=first years students live in one of the collegedormitories=0.40 Who does not live in dormitories=0.60 B=graduation rate of the first year students at thiscollege=0.75 Since the two factors are independent From the independence proprety of the events We have P(A and B)=P(A).P(B)=0.40(0.75)=0.3 2) P(Ac and B)=P(A)=0.60*0.75=0.45 3) P(Ac andBc)=P(Ac)P(Bc)=0.60(0.25)=0.15

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