Answer to Question #302316 in Statistics and Probability for Yen

Question

 From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession. Each ball is placed back in the box before the next draw was made. Let G be a random variable representing the number of green balls that occur. Find the values of the random variable G. 

Answer 1

We let B and G be the random variables representing the number of black and green balls that occur respectively,

Suppose,

1) No green ball occurs for the 3 successions; {BBB}, then, G=0

2) 1 green and 2 black balls occur; {GBB, BGB, BBG} , then, G = 1

3) 2 green and 1 black balls occur; {GGB, GBG,BGG} , then, G = 2

4) 3 green and no black balls occur; {GGG} , then, G = 3

Therefore, the only possible values of the random variable G are 0, 1, 2, 3