Let `A ,B ,C` be three events. If the probability of occurring exactly one event out of `Aa n dBi s1-x ,` out of`Ba n dCi s1-2x ,` out of`Ca n dAi s1-x ,` and that of occuring three events simultaneously is `x^2` , then prove that the probability that atleast one out of A, B, C will occur is greaer than 1/2 .

Let A,B,C be three events.If the probability of occurring exactly one event out of A and B is 1-x, out of B and C is 1-2x, out of C and A is 1-x and that of occurring three events simultaneously is x^(2), then prove that the probability that at least one out of A,B,C . will occur is greater than 1/2 .

For three events A, B and C, P (Exactly one of A or B occurs) = P (Exactly one of B or C occurs) = P (Exactly one of C or A occurs) = (1)/(4) and P(All the three events occurs simultaneously = (1)/(16) . Then the probability that at least one of the events occurs, is :

Let A,B and C be three events such that the probability that exactly one of A and B occurs is (1-k), the probability that exactly one of B and C occurs is (1 –2k), the probability that exactly one of C and A occurs is (1 –K) and the probability of all A, B and C occur simultaneously is k ^(2), where 0 lt k lt 1. Then the probability that at least one of A, B and C occur is:

For the three events A ,B ,a n dC ,P (exactly one of the events AorB occurs)=P (exactly one of the two evens BorC )=P (exactly one of the events CorA occurs)=pa n dP (all the three events occur simultaneously)=p^2w h e r eo

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

For the three events A, B and C, P(exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) =P(exactly one of the events C or A occurs)= p and P(all the three events occur simultaneously) = p^2, where 0ltplt1/2. Then, find the probability of occurrence of at least one of the events A, B and C.