The probability that A speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The…
The probability that A speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is
$\frac{3}{20}$
$\frac{1}{5}$
$\frac{7}{20}$
$\frac{4}{5}$
Solution
$\mathrm{E}_1$ : event denoting that $A$ speaks truth
$\mathrm{E}_2$ : event denoting that $B$ speaks truth
Probability that both contradicts each other $=P\left(E_1 \cap \bar{E}_2\right)+P\left(\bar{E}_1 \cap E_2\right)=\frac{4}{5} \cdot \frac{1}{4}+\frac{1}{5} \cdot \frac{3}{4}=\frac{7}{20}$