Alopecia

Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that:
(a) exactly four men suffer from alopecia.
(b) at most two men suffer from alopecia.

Correct result:

p4 =  0.2627
p =  0.2201

Solution:

C4(8)=(84)=8!4!(84)!=87654321=70 q=45%=45100=0.45 n=8  p4=(n4) q4 (1q)n4=70 0.454 (10.45)84=0.2627
C0(8)=(80)=8!0!(80)!=11=1 C1(8)=(81)=8!1!(81)!=81=8 C2(8)=(82)=8!2!(82)!=8721=28 p0=(n0) q0 (1q)n0=1 0.450 (10.45)800.0084 p1=(n1) q1 (1q)n1=8 0.451 (10.45)810.0548 p2=(n2) q2 (1q)n2=28 0.452 (10.45)820.1569  p=p0+p1+p2=0.0084+0.0548+0.1569=0.2201



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