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The daily production of a factory is 20 articles, of which two are always defect. A sample of four is taken. Let X be the random variable that assigns the number of defect articles in the sample. Calculate:

a)The probability distribution for X when P(x=0), P(X=1) and P(X=2)

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Could you please tell us what you have tried/where you got stuck etc.? –  Patrick Oct 19 '13 at 17:17
    
Bueno, get the probabilities in the sample when there are 0, 1 and 2 defect articles –  Isra McCabe Oct 19 '13 at 17:23

1 Answer 1

I will give you a walk-through of a solution for $\mathbb{Pr}[X=0]$.

Given that there are $20$ articles to choose from, the number of different samples is $\binom{20}{4}$. If we select none of the $2$ defect articles we get $\binom{18}{4}$ different samples. So, $\mathbb{Pr}[X = 0] = \frac{\binom{18}{4}}{\binom{20}{4}}$. Can you figure out the other two probabilities using the same counting technique?

If you are not familiar with binomial coefficients, please read this.

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