Question

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

• A. 0.71
• B. 0.70
• C. 0.51
• D. 0.20

Answer 1

Answer: (A)

Given $\frac{\left(x-10\right)\left(x-50\right)}{\left(x-30\right)}\ge 0$
Let $x\ge 10,x\ge 50$ equation will be true
$\forall x\ge 50$
as $\left(\frac{x-50}{x-30}\right)\ge 0,\forall x\in [10,30)$
$\frac{\left(x-10\right)\left(x-50\right)}{x-30}\ge 0,\forall x\in [10,30)$
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 $x=51+20=71$
$P\left(A\right)=\frac{71}{100}=0.71$