Question

A meeting of envoy was attended by 5 Koreans and 3 Filipinos. If four envoy were selected at random one after the other determine the values of the random variable K representing the number of Koreas.

Answer 1

Four envoy were selected in $\dbinom{8}{4}=70.$

The possible values of the random variable $K$ are $1,2,3,4.$

$$P(K=1)=\dfrac{\dbinom{5}{1}\dbinom{3}{4-1}}{\dbinom{8}{4}}=\dfrac{1}{14}$$

$$P(K=2)=\dfrac{\dbinom{5}{2}\dbinom{3}{4-2}}{\dbinom{8}{4}}=\dfrac{3}{7}$$

$$P(K=3)=\dfrac{\dbinom{5}{3}\dbinom{3}{4-3}}{\dbinom{8}{4}}=\dfrac{3}{7}$$

$$P(K=4)=\dfrac{\dbinom{5}{4}\dbinom{3}{4-4}}{\dbinom{8}{4}}=\dfrac{1}{14}$$