NIMCET 2017 Question Paper with solutions

Question : 71 of 120

Marks: +1, -0

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

${xy}/{xy+(1-x)(1-y)}$
${xy}/{(1-x)(1-y)}$
${(1-x)(1-y)}/{xy+(1-x)(1-y)}$
${x+y}/{xy+(1-x)(1-y)}$

Validate

Solution:

P(A speaks truth) = x
P(B speaks truth) = y
Since, both A and B agree on certain statement
∴ Total probability
= P(A) P(B)+ P(A') P(B')
= xy + (1-x)(1-y)
If statement is true then it means both A and B speaks truth.
∴ Required probability =

{xy}/{xy+(1-x)(1-y)}

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