Answer to Question #121967 in Statistics and Probability for Luqman

Question

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?

Answer 1

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

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

$P(X \ge 2)=\sum_{i=2}^6 {6 \choose x} (\frac {1}{6})^x(\frac {5}{6})^{6-x}$

=0.2632