UPSC NDA Math Model Paper 2

Consider, Let K be the event that both A and B agree,
T be the event that they both A and B speak the truth
⇒ P(T) = xy
L be the event that they both A and B lie.
⇒ P(L) = (1 -x)(1 - y)
To find :The probability that the statement is true =P(

T

L

)
Let K be the event that both of them agree
P(

T

L

)=

P(T)P( K T )

P(T)P( K T )+P(L)P( K L )

⇒P(

T

L

)=

xy

xy+(1−x)(1−y)