Probability

Let H\(_1\), H\(_2\), ..., H\(_n\) be mutually exclusive and exhaustive events with P(H\(_i\)) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1.

Statement 1 : P(H\(_i\) | E) > P(E | H\(_i\)). P(H\(_i\)) for \(i=1,2,...,n\).

Statement 2 : \(\sum\limits_{i = 1}^n {P({H_i}) = 1}\).