Answer to Question #167789 in Statistics and Probability for angela gumasing

Question

recall how to determine the values of the random variable by answering the given problem. Find the values of the ramdon variable Y representing the number of green balls when 2 balls are drawn in succession without replacement from a jar 4 red balls and 5 green balls

Answer 1

Total balls in the jar: 4+5=9

find the probability that the green balls will be 0, 1 and 2 respectively:

$P(Y = 0) = \frac{4}{9} \cdot \frac{3}{8} = \frac{1}{6}$ (both red balls)

$P(Y = 1) = \frac{4}{9} \cdot \frac{5}{8} + \frac{5}{9} \cdot \frac{4}{8} = \frac{5}{9}$ (red ball and green ball or green ball and red ball)

$P(Y = 2) = \frac{5}{9} \cdot \frac{4}{8} = \frac{5}{{18}}$ (both green balls)

we have the distribution series of the random variable Y:

$\begin{matrix} Y&0&1&2\\ p&{\frac{1}{6}}&{\frac{5}{9}}&{\frac{5}{{18}}} \end{matrix}$