Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of Blue balls. Find the values of the random variable Z

Let's denote R - red ball, B - blue ball.

Sample space S is all possible outcomes.

$S=\{RR, RB, BR, BB\}$

The possible values of the random variable $Z$ are $0, 1, 2.$

$\def\arraystretch{1.5} \begin{array}{c:c} Possible \ Outcomes & Z \\ \hline RR & 0 \\ \hdashline RB & 1 \\ \hdashline BR & 1 \\ \hdashline BB & 2 \\ \hdashline \end{array}$

Construct the probability distribution of the random variable

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

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

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

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

$\def\arraystretch{1.5} \begin{array}{c:c} z & 0 & 1 & 2 \\ \hline p(z) & 2/11 & 6/11 & 3/11 \end{array}$