• # question_answer The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact, is A) $\frac{3}{20}$    B)                        $\frac{1}{5}$                    C)        $\frac{7}{20}$                 D)        $\frac{4}{5}$

Solution :

The probability of speaking truth by A, $P(A)=\frac{4}{5}$ The probability of not speaking truth by $A,P(\overline{A})=1-\frac{4}{5}=\frac{1}{5}$. The probability of speaking truth by B, $P(B)=\frac{3}{4}$. The probability of not speaking truth of $B,P(\overline{B})=\frac{1}{4}$ The probability that they contradict each other $=P(\overline{A})\times P(\overline{B})+P(\overline{A})\times P(B)$                 $=\frac{4}{5}\times \frac{1}{4}+\frac{1}{5}\times \frac{3}{4}$                 $=\frac{1}{5}+\frac{3}{20}=\frac{7}{20}$

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