The probability that A speaks the truth is fr | vedclass

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(C) Let $P(A)$ be the probability that $A$ speaks the truth and $P(B)$ be the probability that $B$ speaks the truth.Given: $P(A) = \frac{4}{5}$ and $P

Vedclass · Accepted Answer

$\frac{7}{20}$

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(C) Let $P(A)$ be the probability that $A$ speaks the truth and $P(B)$ be the probability that $B$ speaks the truth.Given: $P(A) = \frac{4}{5}$ and $P(B) = \frac{3}{4}$.Then,the probability that $A$ lies is $P(\bar{A}) = 1 - \frac{4}{5} = \frac{1}{5}$.The probability that $B$ lies is $P(\bar{B}) = 1 - \frac{3}{4} = \frac{1}{4}$.They contradict each other if ($A$ speaks the truth and $B$ lies) $OR$ ($A$ lies and $B$ speaks the truth).Required probability $= P(A) 	imes P(\bar{B}) + P(\bar{A}) 	imes P(B)$.$= (\frac{4}{5} 	imes \frac{1}{4}) + (\frac{1}{5} 	imes \frac{3}{4})$.$= \frac{4}{20} + \frac{3}{20} = \frac{7}{20}$.

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

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