Answer to Question #197415 in Statistics and Probability for HanXiao

Question

Two balls are drawn in succession without replacement from an urn containing 5 white balls and 6 black balls. Let Z be the random variable representing the number of black balls. Construct the probability distribution of the random variable Z.

Possible Outcomes-

Value of the Random Variable Z(Number of Blue Balls)-

Answer 1

$$P(WW)=\dfrac{5}{11}(\dfrac{4}{10})=\dfrac{2}{11}$$

$$P(WB)=\dfrac{5}{11}(\dfrac{6}{10})=\dfrac{3}{11}$$

$$P(BW)=\dfrac{6}{11}(\dfrac{5}{10})=\dfrac{3}{11}$$

$$P(BB)=\dfrac{6}{11}(\dfrac{5}{10})=\dfrac{3}{11}$$

Let $Z=$ Number of Blue Balls. Then

$$\begin{matrix} z & 0 & 1 & 2 \\ \\ p(z) & \dfrac{2}{11} & \dfrac{6}{11} & \dfrac{3}{11} \end{matrix}$$

Check

$$\dfrac{2}{11}+\dfrac{6}{11}+\dfrac{3}{11}=1$$