Let `H_1, H_2,..., H_n` be mutually exclusive events with `P (H_i) > 0, i = 1, 2,.......... n.` Let `E` be any other event with `0 < P (E)` Statement I `P(H_i|E) > P(E|H_i .P(H_i)` for `i=1,2,.......,n` statement II `sum_(i=1)^n P(H_i)=1`

Suppose E_1, E_2 and E_3 be three mutually exclusive events such that P(E_i)=p_i" for " i=1, 2, 3 . P(none of E_1, E_2, E_3 ) equals

Suppose E_1, E_2 and E_3 be three mutually exclusive events such that P(E_i)=p_i" for "i=1, 2, 3 . If p_1, p_2 and p_3 are the roots of 27x^3-27x^2+ax-1=0 the value of a is

Suppose E_1, E_2 and E_3 be three mutually exclusive events such that P(E_i)=p_i" for "i=1, 2, 3 . P(E_1capoverline(E_2))+P(E_2capoverline(E_3))+P(E_3capoverline(E_1)) equals

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

There are n turns each continuous (n+1) balls such that the ithurn contains 'I' white balls and (n+1-i) red balls. Let u_(1) be the event of selecting ith urn, i=1,2,3……..n and W denotes the event of getting a white balls. If P(u_(i)) prop i , where i=1,2,3,........,..n, then lim_(n to oo) P(W) is equal to

If A_1, A_2, …, A_n are n independent events, such that P(A_i)=(1)/(i+1), i=1, 2,…, n , then the probability that none of A_1, A_2, …, A_n occur, is

There are n urns numbered 1 to n . The ith urn contains i white and (n+1-i) black balls. Let E_(i) denote the event of selecting ith urn at random and let W denote the event that the ball drawn is white. If P(E_(i))propi for i=1,2..........,n then lim_(nrarroo) P(W) is

If P(u_i)) oo i , where i = 1, 2, 3, . . ., n then lim_(nrarrw) P(w) is equal to