Among the N =18 advisory members of an education program, A=12 are university fa
ID: 3135433 • Letter: A
Question
Among the N =18 advisory members of an education program, A=12 are university faculty members and the other N -A= 6 are business managers. A random sample of n= 6 advisory members is going to be selected. Use X to denote the number of advisory members who are university faculty members. Keep at least 4 decimal digits if the result has more decimal digits.
A. The probability that exactly 5 advisory members are university faculty members is closest to
B. The probability that all 6 advisory members are university faculty members is closest to
C. The probability that at least 5 advisory members are university faculty members is closest to
D. The probability that at most 4 advisory members are university faculty members is closest to
please answer in detailed explanation for following questions
Explanation / Answer
N=12 are faulty members and N=6 are business managers
A. P(exactly 5 are faulty members)=the 5 will be chosen from 12 faulty members and remaining 1 from 6 business managers
P(A)=(12c5*6c1)/18c6 (18c6 is the total probability to choose 6 from total of 18 members)
=(8*9*10*11*12*6/120)/[(13*14*15*16*17*18)/6!]
=4752/(18564)=0.2555
B. all 6 are faulty members which will be choosen from 12 faulty members
P(B)=12c6/18c6
=(7*8*9*10*11*12/720)/(13*14*15*16*17*18)/6!)
=924/18564=0.04977
C. at least 5 advisory members are university faculty members means either 5 or 6 are faulty would be sum of above 2 probabilities
P(C)=P(5)+P(6)
=(12c5*6c1)/18c6+12c6/18c6
=0.2555+0.04977=0.30527
D. at most 4 advisory members are university faculty members means either 0 or 1 or 2 or 3 or 4 are faulty members
P(D)=P(0)+p(1)+P(2)+P(3)+P(4)
=(6c6+12c1*6c5+12c2*6c4+12c3*6c3+12c4*6c2)/18c6
=(1+12*6+66*15+220*20+495*15)/18564
=(1+72+990+4400+7425)/18564=0.6942
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