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
0.38
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B
0.94
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C
0.54
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D
0.56
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Solution
The correct option is C0.54 Given, P(A speaks truth)=0.6,P(B speaks truth)=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 ⇒P(E)=P(A speaks truth)⋅P(B speaks truth)+P(A lies)⋅P(B lies) ⇒P(E)=0.6×0.7+(1−0.6)(1−0.7) =0.42+0.12 =0.54