Answer to Question #297429 in Statistics and Probability for von

Question

Four balls are drawn in succession without replacement from an urn containing 4 red balls, 3 blue balls and 3 yellow balls. Let Z be the random variable representing the number of blue balls.

Answer 1

There are 4 red, 3 blue and 3 yellow balls. Let the random variable $Z$ represent the number of blue balls drawn, Then $Z$ may take on the values, 0,1,2,3 as described below.

For, $Z=0$, we will have 0 blue balls and 4 non-blue balls.

For, $Z=1,$ we will have 1 blue ball and 3 non-blue balls.

For, $Z=2,$ we will have 2 blue balls and 2 non-blue balls.

For, $Z=3,$ we will have 3 blue balls and 1 non-blue ball.

The number of blue balls cannot be 4 because we only have 3 blue balls.

So, the random variable $Z$ is a discrete random variable which may take on the values 0,1,2,3.