NIMCET 2023 — Mathematics PYQ

Probability A speaks truth $P(AT)=\frac{60}{100}=\frac{3}{5}$

Probability A speaks lie $P(AL)=\frac{40}{100}=\frac{2}{5}$

Probability B speaks truth $P(BT)=\frac{50}{100}=\frac{1}{2}$
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Probability George speaks lie $P(BL)=\frac{50}{100}=\frac{1}{2}$

Probability that they contradict each other stating the same fact $=P(AT\cap BL)+P(AL\cap BT)$

$=\frac{3}{5}\times \frac{1}{2}+\frac{2}{5}\times \frac{1}{2}=\frac{1}{2}$
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