A number x is chosen at random from the set {1, 2, 3, 4, ...., 100}. Define the event A : A= the chosen number x satisfies $\frac{(x-10)(x-50)}{(x-30)}\ge 0$  Then $P\left(A\right)$ is

Given $\frac{(x-10)(x-50)}{(x-30)}\ge 0$   Let  $x\ge 10,x\ge 50$ equation will be true $\forall x\ge 50$   as 
$\begin{array}{l}\left(\frac{x-50}{x-30}\right)\ge 0,\\ \forall x\in [10,30)\\ \frac{(x-10)(x-50)}{x-30}\ge 0\\ \forall x\in [10,30)\end{array}$
Total value of x between 10 to 30 is 20. Total values of x between 50 to 100 including 50 and 100 is 51. Total values of x = 51 + 20 = 71