Question

The probability of A speaks truth 4/5 while B is 3/4. The probability that they contradict each other when asked to speak on a fact is

Answer 1

let
$p |1| = \frac{4}{5} ( a \: speaks \: truth) \\ q |1| = \frac{1}{5} (a \: lie) \\ \\ similarly \: for \: b \\ p |2| = \frac{3}{4} \\ q |2| = \frac{1}{4} \\ prob \: of \: contradiction \: \\ p = p |1| q |2| + p |2| q |1| \\ = (\frac{4}{5} \times \frac{1}{4} ) + ( \frac{3}{4} \times \frac{1}{5} )$
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