A box contains 4 yellow (Y) and 8 Pink balls. Six balls will be selected in the box. Determine the values of random variable P representing the number of pink balls.

There  are 4 yellow (Y) and 8 Pink (P) balls. Total number of balls is 4+8=12 balls. 6 balls are selected at random.

Let $P$ denote the number of pink balls selected then $P$ is a discrete random variable which may take on the values, 0,1,2,3,4,5,6 as described below.

The following a few possible sample points are described below to show the number of pink balls selected.

1. YYYYYY-  In this sample point the number of pink balls is $P=0$
2. YYYYYP- In this sample point, the number of pink balls is $P=1$
3. YYYYPP- In this sample point, the number of pink balls is $P=2$
4. YYYPPP- In this sample point, the  number of pink balls is $P=3$
5. YYPPPP- In this sample point, the number of pink balls is $P=4$
6. YPPPPP- In this sample point, the number of pink balls is $P=5$
7. PPPPPP- Here, the number of pink balls selected is $P=6$

Therefore, $p=\{0,1,2,3,4,5,6\}$