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

given $\frac{(x-10)(x-50)}{x-30}\ge 0\text{ Let }x\ge 10,x\ge 50$ equation will be true , $\mathrm{\forall }x\ge 50$

As $\left(\frac{x-10}{x-30}\right)\ge 0,\mathrm{\forall }x\in [10,30) and \frac{(x-10)(x-50)}{x-30}\ge 0\mathrm{\forall }x\in [50,100]$

Total values between 10 to 30 is 20 and  total values between 50 to 100 including             

50 and 100 is 51 

Total values of =51+20=71 

$p\left(A\right)=\frac{71}{100}=0.71$