Answer to Question #121967 in Statistics and Probability for Luqman

Question #121967
Super bikes arrive in a 12 lot showroom. Inspections are carried out on six out of every 12. For
one lot, it is known 2 out of 12 do not meet the safety standards prescribed. What is the
probability that at least 2 out of the 6 that were tested from that lot will not meet safety
standards?
1
Expert's answer
2020-06-15T14:33:20-0400

The probability that a bike will meet safety standards is 212=16\frac {2}{12}=\frac {1}{6}

P(X=x)=(nx)pxqnxP(X=x) ={n\choose x} p^xq^{n-x}

P(X2)=i=26(6x)(16)x(56)6xP(X \ge 2)=\sum_{i=2}^6 {6 \choose x} (\frac {1}{6})^x(\frac {5}{6})^{6-x}

=0.2632


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