Question

A natural number is selected at random from the set X = {$x:1\le x\le 100$}. The probability that the number satisfies the inequation $x^2-13x\le 30$, is

• A. $\frac{9}{50}$
• B. $\frac{3}{20}$
• C. $\frac{2}{11}$
• D. $\frac{7}{9}$

Answer 1

The correct option is B $\frac{3}{20}$

$x^2-13x\le 30\Rightarrow (x-15)(x+2)\le 0$
$\Rightarrow x\in (-2,15)$
Hence number of favourable cases $n\left(E\right)=15$ Also number of sample space is $=100$
Hence required probability is $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{15}{100}=\frac{3}{20}$