Answer to Question #337424 in Statistics and Probability for ana

Question

Two balls are drawn in succession without replacement from a box containing 9 black balls (B) and 7 white balls (W). Let Z be the random variable representing the number of white balls. Possible Outcomes Value of the Random Variable Z Number of White Balls (Z) Probab

Answer 1

Possible outcomes of the Random Variable Z are: $0,1,2.$

$$P(Z=0)=P(BB)$$

$$=\dfrac{9}{16}(\dfrac{8}{15})=\dfrac{3}{10}$$

$$P(Z=1)=P(BW)+P(WB)$$

$$=\dfrac{9}{16}(\dfrac{7}{15})+\dfrac{7}{16}(\dfrac{9}{15})=\dfrac{21}{40}$$

$$P(Z=2)=P(WW)$$

$$=\dfrac{7}{16}(\dfrac{6}{15})=\dfrac{7}{40}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} z & 0 & 1 & 2 \\ \hline p(z) & 3/10 & 21/40 & 7/40 \\ \end{array}$$