Answer to Question #224194 in Statistics and Probability for Reyad

Question #224194

A lot consists of (6+a) articles, 3 with minor defects, and 3 with major defects. The ‘a’

articles are chosen at random from the lot without replacement. Compute the

probability by using basic probability concepts, both articles are good.


1
Expert's answer
2021-08-10T11:55:16-0400

A lot consists of (6+a) articles, 6 with defects.

aa articles are chosen at random from the lot without replacement.

Suppose that XX be the number of articles with defects from aa articles chosen


P(X=0)=(aa)(60)(6+aa)=6!a!(6+a)!P(X=0)=\dfrac{\dbinom{a}{a}\dbinom{6}{0}}{\dbinom{6+a}{a}}=\dfrac{6!a!}{(6+a)!}

If 22 articles are chosen at random from the lot without replacement (a2).(a\geq2).

Suppose that YY be the number of articles with defects from 22 articles chosen


P(Y=0)=(a2)(60)(6+a2)=a!6!a!2!(a2)!(6+a)!P(Y=0)=\dfrac{\dbinom{a}{2}\dbinom{6}{0}}{\dbinom{6+a}{2}}=\dfrac{a!6!a!}{2!(a-2)!(6+a)!}


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