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Question

A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact?

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Solution

Let
A= Event that A speaks the truth
B= Event that B speaks the truth
Then,
P(A)=75100=34
P(B)=90100=910
P(Alie)= 134=14
P(Blie)= 1910=110
Now,
A and B contradict each other =[A lies and B true] or [B true and B lies]
=P(A).P(B-lie) + P(A-lie).P(B)
=34×110+14×910=1240=310
=310×100%=30%

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