Answer to Question #225199 in Statistics and Probability for Reyad

Question

A lot consists of (6+55) articles, 3 with minor defects, and 3 with major defects. 55

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

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

Answer 1

Let $X=$ the number of defective items in the sample.

$$P(X=0)=\dfrac{\dbinom{6}{0}\dbinom{55}{55}}{\dbinom{55+6}{55}}=\dfrac{1}{55525372}$$ $$P(X=1)=\dfrac{\dbinom{6}{1}\dbinom{55}{54}}{\dbinom{55+6}{55}}=\dfrac{6(55)}{55525372}=\dfrac{330}{55525372}$$ $$P(X\leq1)=P(X=0)+P(X=1)$$ $$=\dfrac{1}{55525372}+\dfrac{330}{55525372}=\dfrac{331}{55525372}$$

$$\approx0.00000596$$