Question

A meeting of envoys was attended by 4 Koreans and 2 Filipinos. If three

envoys were selected at random one after the other, determine the values

of the random variable F representing the number of Filipinos.

Answer 1

$F=0:\;p=\frac{4}{6}*\frac{3}{5}*\frac{2}{4}=\frac{1}{5}.$

$F=1:\;p=\frac{4}{6}*\frac{3}{5}*\frac{2}{4}+\frac{4}{6}*\frac{2}{5}*\frac{3}{4}+\frac{2}{6}*\frac{4}{5}*\frac{3}{4}=\frac{3}{5}.$

$F=2:\;p=\frac{2}{6}*\frac{1}{5}*\frac{4}{4}+\frac{2}{6}*\frac{4}{5}*\frac{1}{4}+\frac{4}{6}*\frac{2}{5}*\frac{1}{4}=\frac{1}{5}.$