Answer to Question #309634 in Statistics and Probability for Jonaisa

Question

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. Make a table to show the values of the random variable.

Answer 1

Solution

When two successive balls are drawn there are three possibilities

1. Two red balls are drawn and hence $Z=0$
2. One red and one blue ball are drawn and hence $Z=1$
3. Two blue balls are drawn and hence $Z=2$

The Probability distribution of Z values is as shown

$\def\arraystretch{1.5}\begin{array}{c:c} Z-Value& Probability \\\hline0&\frac{2}{11}\\\hdashline1&\frac{6}{11}\\\hdashline2&\frac{3}{11}\\\hline\end{array}$