A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x+ 1 x 2 ?

Step-by-step solution

aligned & x+ 1 x 2 x^2+1 x -2 0 & x^2-2 x+1 x 0 (x-1)^2 x 0 & - - 0 & x (0, )- 1 and x N & n= 2,3,4, . n) aligned aligned & n(E)=n-1 & P(E)= n-1 n aligned