A speaks truth in 60 percent of cases and B s | vedclass

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Question

(B) Let $A$ be the event that $A$ speaks the truth and $B$ be the event that $B$ speaks the truth.Given probabilities are $P(A) = 0.6$ and $P(B) = 0.7

Vedclass · Accepted Answer

$0.54$

Vedclass · Answer

(B) Let $A$ be the event that $A$ speaks the truth and $B$ be the event that $B$ speaks the truth.Given probabilities are $P(A) = 0.6$ and $P(B) = 0.7$.Therefore,the probability that $A$ lies is $P(A') = 1 - 0.6 = 0.4$.The probability that $B$ lies is $P(B') = 1 - 0.7 = 0.3$.They will say the same thing if both speak the truth or both tell a lie.Probability of saying the same thing $= P(A) 	imes P(B) + P(A') 	imes P(B')$.$= (0.6 	imes 0.7) + (0.4 	imes 0.3)$.$= 0.42 + 0.12 = 0.54$.

$A$ speaks truth in $60$ percent of cases and $B$ speaks truth in $70$ percent of cases. The probability that they will say the same thing while describing a single event is

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