Question

A speaks truth in 80% cases and B speaks truth in 90% cases. In what percentage of cases are they likely to agree with each other in stating the same fact ?

Answer 1

$P\left(A\right)=\frac{80}{100}=\frac{4}{5},P\left(B\right)=\frac{90}{100}=\frac{9}{10}$

P(Agree) = P(Both speaking truth or both speaking lie)

$=P\left(ABor\overline{AB}\right)$

$=P\left(A\right)P\left(B\right)orP\left(\overline{A}\right)P\left(\overline{B}\right)$

$=\frac{4}{5}\times \frac{9}{10}+\frac{1}{5}\times \frac{1}{10}$

$=\frac{37}{50}=\frac{74}{100}=70\%$.