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
Answer : option (B)
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