IIT JEE Advanced 2007 Paper 1

Statement-1: If P(HinE) = 0 for some i, then
P(

Hi

E

) = P(

E

Hi

) = 0
If P(HinE) ≠ 0 for all i = 1 , 2 , 3 , ... , n, then
P(

Hi

E

) =

P(HinE)

P(Hi)

×

P(Hi)

P(E)

=

P( E Hi )×P(Hi)

P(E)

> P(

E

Hi

)×P(Hi)
Hence, Statement-1 may not always be true.
Statement-2: Clearly, we can write as
K1 ∪ H2 ∪ H3 ∪ ... ∪ Hn = S
⇒ P(H1)+P(H2)+ ... + P(Hn) = 1
Hence, Statement-2 is true.