Question

Write the probability distribution of a random variable R representing numbers of red ball when 3 balls are drawn in succession without replacement from a jar containing 4 red and blue balls

Answer 1

We can pull out three red balls, or two red and one blue. To find the probability of three red balls, we need to repeat and multiply three times: divide the number of red balls by the total number of balls and pull out the red ball:

$P(3\text{ red})=\frac{4}{5}\cdot\frac{3}{4}\cdot\frac{2}{3}=0.4\\ P(2\text{ red})=1-P(3\text{ red})=0.6$

We can write down the probability distribution:

$R=\begin{pmatrix} 2 & 3 \\ 0.6 & 0.4 \end{pmatrix}$