1http://targetiit.com/iit-jee-forum/posts/value-of-testimony-12822.html
A and B are two independent witnesses (i.e there is no collusion between them) in a case.The probability that A,B speaks truths are x and y respectively.A and B agree in a certain statement.Find the probability that the statement is true.
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5 Answers
3brother frankly i dunno how to apply baye's theorem.dats y i posted.My dbt is the statement can be true or false na.how to include dat in calculation.
13Assuming tht the Events of St. being False/True are equally likely.
CASE-I
Statement is True.
i) Both say its true. P(i)=1/2*xy
ii) Both say its false. P(ii)=1/2*(1-x)(1-y)
CASE-II Statement is False.
a) Both say its false. P(a)=1/2*xy
b) Both say its True. P(b)=1/2*(1-x)(1-y)
Favourable cases - i),ii).
So, P(tht the statement was true)=
\frac{P(i)+P(ii)}{P(i)+P(ii)+P(a)+P(b)} = \frac{1}{2}
Hoping tht i didn't misinterpret the Qn [1]
3brother there are still other cases na,like one is true and the other is false.I think this also shud be included in the total probability.And how to get the logic by venn diagram,Sorry for asking this but i cant visualize this one.
13
Qn says -"Both agree in a certain statement" i.e. they can't have divergent views, like one says St. is false n the other says tht St. is true.
Thts why, those cases needn't be considered.
Also, i forgot to take in the prob. of the St. being True/False... though it will eventually get cancelled, but editing now.