Question

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. Find the probability distribution of the number of black balls.

Answer 1

$P(X=0)=\frac{4}{7}*\frac{3}{6}=\frac{2}{7}.$

$P(X=1)=\frac{4}{7}*\frac{3}{6}+\frac{3}{7}*\frac{4}{6}=\frac{4}{7}.$

$P(X=0)=\frac{3}{7}*\frac{2}{6}=\frac{1}{7}.$