NIMCET 2009 Question Paper with solutions

Question : 13 of 120

Marks: +1, -0

A and B are independent witnesses in a case. The probability that A speaks the truth is 'x' and that B speaks the truth is ' y. If A and B agree on a certain statement, the probability that the statement is true is

$\;{x Y}/{x y+(1-x)(1-y)}$
$\;{x y}/{(1-x)(1-y)}$
$\;{(1-x)(1-y)}/{x y+(1-x)(1-y)}$
$\;{(1-x)(1-y)}/{x y}$

Validate

Solution:

Probability (statement is true | Agreement)

=\;{P(\;\text " true statement and agreement "\;)}/{P(\;\text " Agreement "\;)}

=\;{x ⋅ y}/{x ⋅ y+(1-x⟩(1-y)}

Note: Agreement can be there if both are speaking truth or both are telling a lie.

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