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Question

A speaks truth in 75% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

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Solution

Let A= event where A speaks the truth.
B= event where B speaks the truth.
P(A)=75%=0.75
P(B)=80%=0.80
P(A)=0.25
P(B)=0.20
where, A and B are events when they lie.
For them to contradict each other, one has to lie and the other has to be truthful.
=(0.75)(0.2)+(0.8)(0.25)
=0.35=35%

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