NIMCET 2023 Question Paper with solutions

Probability A speaks truth P(AT)
$=\frac{60}{100}=\frac{3}{5}$
$\Rightarrow$ Probability A speaks lie $\mathrm{P}\left(\mathrm{AL}\right)$
$=\frac{40}{100}=\frac{2}{5}$
Probability B speaks truth $\mathrm{P}\left(\mathrm{BT}\right)$
$=\frac{50}{100}=\frac{1}{2}$
$\Rightarrow$ Probability George speaks lie P(BL)
$=\frac{50}{100}=\frac{1}{2}$
Probability that they contradict each other stating the same fact
$=\mathrm{P}\left(\mathrm{AT}\cap \mathrm{BL}\right)+\mathrm{P}\left(\mathrm{AL}\cap \mathrm{BT}\right)$
$=\frac{3}{5}\times \frac{1}{2}+\frac{2}{5}\times \frac{1}{2}=\frac{1}{2}$