for three independent events A , & C , probability of A to occur is a , probability of none of them to occur is b and probability of atleast 1 of them not to occur is c .If p denotes the probability that C occurs but neither A nor B occurs , prove that p satisfies

ap² + [ab - ( 1 - a)(a + c - 1)]p + b(1 - a)( 1 - c) = 0

 

also show

 

c > (1 - a)² + ab / 1 - a