UPSC NDA Math Model Paper 10

Let X be the event that 'Prabhu reports that six occurs in throwing of the die and let E1 be the event that six occurs and E2 be the event that six does not occur.
⇒P(E1)=1∕6 and P(E2)=1−P(E1)=5∕6
P(X|E1)= Probability 'Prabhu speaks truth' =3∕4
P(X|E2)= Probability 'Prabhu does not speaks truth' =1−P(X|E1)=1∕4
Here, we have to find the value of P(E1|X)
As we know that according to bayes' theorem: P(Ei|A)=

P(Ei)×P(A|Ei)

n ∑ i=1 P(Ei)×P(A|Ei)

, i=1,2,......,n
⇒P(E1|X)=

1 6 . 3 4

[ 1 6 . 3 4 + 5 6 . 1 4 ]

=

3

8