QJEEM22Ma2936: JEE Main 2022 Mathematics - Class 12 JEEM22Ma2936 Solution: A bag contains 4 white and 6 black balls. Three balls are drawn …

$X =$ Number of white ball drawn

$P(X = 0) = {{{}^6{C_3}} \over {{}^{10}{C_3}}} = {1 \over 6}$

$P(X = 1) = {{{}^6{C_2} \times {}^4{C_1}} \over {{}^{10}{C_3}}} = {1 \over 2},$

$P(X = 2) = {{{}^6{C_1} \times {}^4{C_2}} \over {{}^{10}{C_3}}} = {3 \over {10}}$

and $P(X = 3) = {{{}^6{C_0} \times {}^4{C_3}} \over {{}^{10}{C_3}}} = {1 \over {30}}$

Variance $= {\sigma ^2} = \sum {{P_i}X_i^2 - {{\left( {\sum {{P_i}{X_i}} } \right)}^2}}$

${\sigma ^2} = {1 \over 2} + {{12} \over {10}} + {3 \over {10}} - {\left( {{1 \over 2} + {6 \over {10}} + {1 \over {10}}} \right)^2}$

$= {{56} \over {100}}$

$100{\sigma ^2} = 56.$