Question

Two balls are drawn in succession without replacement from the urn containing 5 yellow balls and 6 green balls. Let Z be the random variable representing the number of green balls. Construct a probability distribution of Z in tabular, graphical, and equation form.

Answer 1

Given,

5 yellow balls and 6 green balls.

Total=11

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 green balls SO both balls are yellow.

$P(Z=0)=\dfrac{^5C_2}{^{11}C_2}=0.18$

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

$P(Z=1)=\dfrac{5}{11}\times \dfrac{6}{10}+\dfrac{6}{11}\times \dfrac{5}{10}=0.545$

When both balls are green.

$P(Z=2)=\dfrac{^6C_2}{^{11}C_2}=0.272$

Probability Distribution table is-

Graphically PD is-

Equation form of PD is-

$P(x)=0.09x^2+0.45x+0.18$