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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
0.38
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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 C 0.54
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+(10.6)(10.7)
=0.42+0.12
=0.54

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