Q70 / 150 · MHT CET 2021 (21 Sep Shift 1) · Mathematics
In a meeting $60 \%$ of the members favour and $40 \%$ oppose a certain proposal. A member is selected at random and we take $\mathrm{X}=0$ if the opposed and $\mathrm{X}=1$ if he is in favour, then Var $\mathrm{X}=$
- A0.36
- Correct answerB0.24
- C0.6
- D0.06
Solution
$$
\text { From the given data, we write }
$$
$$ \text { Variance }=\Sigma \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-\left(\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\right)^2=0.6-(0.6)^2=0.6-0.36=0.24 $$
$$ \text { Variance }=\Sigma \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}^2-\left(\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\right)^2=0.6-(0.6)^2=0.6-0.36=0.24 $$
Hence, the correct answer is option: 'B'.