Answer to Question #211441 in Statistics and Probability for Hammad

Question

The names of 5 men and 5 women are written on slips of paper. Four names are drawn. 

Find the probability using hyper geometric distribution that 2 are men and 2 are 

women?

Answer 1

Let $X=$the number of men names drawn.

$$P(X=x)=\dfrac{\dbinom{k}{x}\dbinom{N-k}{n-x}}{\dbinom{N}{n}}$$

Given $k=5, N=5+5=10, n=4.$

$$P(X=2)=\dfrac{\dbinom{5}{2}\dbinom{5}{4-2}}{\dbinom{10}{4}}=\dfrac{10(10)}{210}=\dfrac{10}{21}$$