Question

$A$ speaks truth in $60$% cases, $B$ in $70$% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

Answer 1

Two cases when both will contradict on the same fact is
1) A speaking truth and B speaking lie
=> $P=0.6\times 0.3$
2) A speaking lie and B speaking truth
=> P $=0.4\times 0.7$
Therefore
$P($contradiction$)=P(1)+P(2)$
$=0.46$