Question

A speaks the truth in 60% of the cases, while B is 40% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?

Answer 1

A speaks truth `P(A) = 60/100`, `P(A') = 40/100`

B speaks truth `P(B) = 40/100`, `P(B') = 60/100`

they contradict each other = `P(A).(B') + P(A') . P(B)`

`= 60/10 xx 60/100 + 40/100 xx 40/100`

`= (3600+1600)/10000`

`= 5200/10000`

`= 52/100`

% of cases they likey to contradict each other = `52/100 xx 100 = 52%`