Correct Answer -
`variance =(400)/(2873)`
Let X be the number of kings. Then, X=0, 1 or 2.
P(X=0)=P(none is a king)=P(both are non-kings)
`=(""^(48)C_(2))/(""^(52)C_(2))=((48xx47)/(2)xx(2)/(52xx51))=(188)/(221).`
P(X=1)=P(one king and one non-king)
`=(""^(4)C_(1)xx""^(48)C_(1))/(""^(52)C_(2))=(4xx48xx(2)/(52xx51))=(32)/(221).`
P(X=2)=P(both are kings)
`=(""^(4)C_(2))/(""^(52)C_(2))=((4xx3)/(2xx1)xx(2xx1)/(52xx51))=(1)/(221).`
Thus, we have
