Question

A box contains 5 green and 2 blue dice.Four dice are chosen one after the other .Determine the values of the random variable G representing the number of green dice.

Answer 1

The possible values of the random variable $G$ representing the number of green dice are

$2, 3, 4.$

$$P(G=2)=\dfrac{\dbinom{5}{2}\dbinom{2}{4-2}}{\dbinom{5+2}{4}}=\dfrac{10(1)}{35}=\dfrac{2}{7}$$ $$P(G=3)=\dfrac{\dbinom{5}{3}\dbinom{2}{4-3}}{\dbinom{5+2}{4}}=\dfrac{10(2)}{35}=\dfrac{4}{7}$$ $$P(G=4)=\dfrac{\dbinom{5}{4}\dbinom{2}{4-4}}{\dbinom{5+2}{4}}=\dfrac{5(1)}{35}=\dfrac{1}{7}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} g & 2 & 3 & 4 \\ \hline P(g) & 2/7 & 4/7 & 1/7 \\ \end{array}$$