Records indicate 90% error-free. If eight records are randomly selected, what is the probability that at least two records have no errors?

Correct answer:

p =  0.9999993

Step-by-step explanation:

q=90%=10090=0.9  C2(8)=(28)=2!(82)!8!=2187=28  p2=(28) q2 (1q)82=28 0.92 (10.9)822.268105  C3(8)=(38)=3!(83)!8!=321876=56  p3=(38) q3 (1q)83=56 0.93 (10.9)830.0004  C4(8)=(48)=4!(84)!8!=43218765=70  p4=(48) q4 (1q)84=70 0.94 (10.9)840.0046  C5(8)=(58)=5!(85)!8!=321876=56  p5=(58) q5 (1q)85=56 0.95 (10.9)850.0331  C6(8)=(68)=6!(86)!8!=2187=28  p6=(68) q6 (1q)86=28 0.96 (10.9)860.1488  C7(8)=(78)=7!(87)!8!=18=8  p7=(78) q7 (1q)87=8 0.97 (10.9)870.3826  C8(8)=(88)=8!(88)!8!=11=1  p8=(88) q8 (1q)88=1 0.98 (10.9)880.4305 p=p2+p3+p4+p5+p6+p7+p8=2.268105+0.0004+0.0046+0.0331+0.1488+0.3826+0.4305=0.9999993

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