Answer to Question #174242 in Statistics and Probability for Clark John

Question

In a box are 2 balls - one white and one yellow. Two balls are picked one at a time with replacement. Let X be the random variable representing the number of white balls. Find the values of the random variable X.

Answer 1

In a box there are $2$ balls -$1$ white and $1$ yellow.

Two balls are drawn one at a time with replacement.

Therefore two balls can be drawn such a way

(a) First drawn ball is yellow and then second drawn ball is yellow.

(b) First drawn ball is yellow and then second drawn ball is white or First drawn ball is white and then second drawn ball is yellow.

(c) First drawn ball is white and then second drawn ball is white.

Let $X$ be a random variable representing number of white balls.

Then $X$ can take the values $0,1,2.$

Now $P(X=0)=$ probability of getting no white balls $=(\frac{1}{2}×\frac{1}{2})=\frac{1}{4}$

$P(X=1)=$ probability of getting one white ball $=[(\frac{1}{2}×\frac{1}{2})+(\frac{1}{2}×\frac{1}{2})]=\frac{1}{2}$

$P(X=2)=$ probability of getting two white balls $=(\frac{1}{2}×\frac{1}{2})=\frac{1}{4}$

Which are the required values of random variable $X.$