Answer to Question #301716 in Statistics and Probability for lyn

Question

A meeting of consuls was attended by 4 Chinese and 2 Japanese. If three consuls where selected at random one after the other, determine the values of the random variable J representing the number of Japanese. 

Answer 1

$$4+2=6$$

There are $\dbinom{6}{3}=20$ possible outcomes.

The possible values of $J$ are $0,1,2.$

$$P(J=0)=\dfrac{\dbinom{2}{0}\dbinom{4}{3-0}}{\dbinom{6}{3}}=\dfrac{1(4)}{20}=\dfrac{1}{5}$$

$$P(J=1)=\dfrac{\dbinom{2}{1}\dbinom{4}{3-1}}{\dbinom{6}{3}}=\dfrac{2(6)}{20}=\dfrac{3}{5}$$

$$P(J=2)=\dfrac{\dbinom{2}{2}\dbinom{4}{3-2}}{\dbinom{10}{4}}=\dfrac{1(4)}{20}=\dfrac{1}{5}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} j & 0 & 1 & 2 \\ \hline p(j) & 1/5 & 3/5 & 1/5 \end{array}$$