10. According to the record of the registrar\'s office at a state university, 35
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10. According to the record of the registrar's office at a state university, 35% of the are senior Among the 3smo ng ine freshmon studentsare freshmen, freshman, 25% are sophomore, 16% are junior and the rest f 8omores, juniors and seniors, the portion of students who live in the dormitory are. %, 60%, 30% and 20%. [10 pts] a If a randomly selected student lives in the dormitory. what is the probability that the freshman? b. If a randomly selected student lives freshman? in the dormitory, what is the probability that the student is not aExplanation / Answer
P(F)=0.35
P(S)=0.25
P(J)=0.16
P(se)=0.24
P(D/F)=0.80
P(D/S)=0.60
P(D/J)=0.30
P(D/se)=0.20
(a) If a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?
Ans:P(F/D)=P(F)P(D/F)/P(F)P(D/F)+P(S)P(D/S)+P(J)P(D/J)+P(se)P(D/se)
=0.80*0.35/(0.35)(0.80)+(0.25)(0.60)+(0.16)(0.30)+(0.24)(0.20)
=0.5323
the probability that the student is a freshman is 0.5323
(b) If a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman
Sol:1-P(F/D)=1-0.5323
=0.4677
the probability that the student is not a freshman is 0.4677
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