Question

Two persons $A,B$ speaks truth with probabilities $0.6$ and $0.7$ respectively. The probability that they will say the same thing while describing a single event is:

• A. $0.56$
• B. $0.54$
• C. $0.38$
• D. $0.94$

Answer 1

The correct option is B $0.54$

Given,
$P\left(A\text{speaks truth}\right)=0.6,P\left(B\text{speaks truth}\right)=0.7$

They can say same thing only when both are speaking truth or both lying
Let $E$ be the event of both of them speaking same about an event
$\Rightarrow P\left(E\right)=P\left(A\text{speaks truth}\right)\cdot P\left(B\text{speaks truth}\right)+P\left(A\text{lies}\right)\cdot P\left(B\text{lies}\right)$
$\Rightarrow P\left(E\right)=0.6\times 0.7+(1-0.6)(1-0.7)$
$=0.42+0.12$
$=0.54$