Question

a meeting of envoys was attended by 4 americans and 5 filipinos. If 6 envoys were selected at random one after the other, determine the values of the random variable F representing the number of filipinos

Answer 1

The possible values of the random variable F representing the number of filipinos are 2, 3, 4 ,5.

$$P(F=2)=\dfrac{\dbinom{4}{4}\dbinom{5}{2}}{\dbinom{4+5}{6}}=\dfrac{10}{84}$$

$$P(F=3)=\dfrac{\dbinom{4}{3}\dbinom{5}{3}}{\dbinom{4+5}{6}}=\dfrac{40}{84}$$

$$P(F=4)=\dfrac{\dbinom{4}{2}\dbinom{5}{4}}{\dbinom{4+5}{6}}=\dfrac{30}{84}$$

$$P(F=5)=\dfrac{\dbinom{4}{1}\dbinom{5}{5}}{\dbinom{4+5}{6}}=\dfrac{4}{84}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} f & 2 & 3 & 4 & 5 \\ \hline p(f) & 10/84 & 40/84 & 30/84 & 4/84 & f \\ \end{array}$$