# A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single even is

Question : A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single even is

(A) 0.56

(B) 0.54

(C) 0.38

(D) 0.94

Solution :

Consider the following events:

X: A speaks truth

Y: B speaks truth

Then, P(X)= 60/100 = 3/5 and P(Y)= 70/100 = 7/10

For the required event, either both of them should speak the truth or both of them should tell a lie.
Thus, the required probability is

P((X n Y) U (X’ n Y’)) = P(X n Y) + P(X’ n Y’)

= P(X) P(Y) + P(X’) P(Y’)

=$\dfrac{3}{5}\times \dfrac{7}{10}+\left( 1-\dfrac{3}{5}\right) \left( 1-\dfrac{7}{10}\right)$

=0.54

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