Question

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R

Answer 1

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

Sample space S is all possible outcomes.

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

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

We will assume that the probability of getting heads and tails is the same:

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

Construct the probability distribution of the random variable

$$P(BB)=\dfrac{5}{9}(\dfrac{4}{8})=\dfrac{5}{18}$$

$$P(BR)=\dfrac{5}{9}(\dfrac{4}{8})=\dfrac{5}{18}$$

$$P(RB)=\dfrac{4}{9}(\dfrac{5}{8})=\dfrac{5}{18}$$

$$P(RR)=\dfrac{4}{9}(\dfrac{3}{8})=\dfrac{3}{18}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} r & 0 & 1 & 2 \\ \hline p(r) & 5/18 & 5/9 & 3/18 \end{array}$$