Question

Two balls are drawn in succession without replacement from an urn containing 6 green balls and 6 yellow balls. Let Y be the random variable representing the number of yellow balls. Find the values of the random variable Y

Answer 1

Given,

6 yellow balls and 6 green balls.

Total=12

Z is a random variable So value of Z can be 0,1 or 2 as two balls are drawn in succession.

When there is 0 yellow balls So both balls are green.

$P(Z=0)=\dfrac{^6C_2}{^{12}C_2}=0.23$

Now If there is one yellow ball ,This can be done in two ways either green first then yellow or vice versa.

$P(Z=1)=\dfrac{6}{12}\times \dfrac{6}{11}+\dfrac{6}{12}\times \dfrac{6}{11}=0.545$

When both balls are yellow.

$P(Z=2)=\dfrac{^6C_2}{^{12}C_2}=0.23$

Probability Distribution table is-