Question

1. Two balls are drawn in succession without replacement from an urn containing

2 green balls and 6 yellow balls. Let M be the random variable representing the

number of yellow balls.

a. What are the possible values of this random variable (range space)?

b. Construct a probability distribution.

Answer 1

Given,

2 Green balls and 6 yellow balls

Let G denotes green ball and Y denotes yellow ball

and M be the random variable representing the number of yellow balls

So,

Possible values:

Case1:

when M=2 means the probability of getting 2 yellow balls when we draw out the balls one at a time is:

$P(M_1)=\dfrac{6}{8}\times \dfrac{5}{7}=\dfrac{30}{56}$

Case2:

When M=1 and first ball drawn is yellow and second ball drawn is green

Probability $P(M_2)=\dfrac{6}{8}\times\dfrac{2}{7}=\dfrac{12}{56}$

Case3:

When M=1 and first ball drawn is green and second ball drawn is yellow

Probability $P(M_3)=\dfrac{2}{8}\times\dfrac{6}{7}=\dfrac{12}{56}$

Case4:

When M=0 and both the balls drawn are green

Probability P$P(M_4)=\dfrac{2}{8}\times\dfrac{1}{7}=\dfrac{2}{56}$

Probability distribution: