Question

A natural number $x$ is chosen at random from 150 natural numbers.The probability that
$\frac{x^2-70x+1200}{x-35}<0$ is

• A. $\frac{23}{30}$
• B. $\frac{1}{50}$
• C. $\frac{11}{50}$
• D. None of these

Answer 1

The correct option is C $\frac{11}{50}$

Total number of case $=150$
$\frac{x^2-70x+1200}{x-35}<0$
$\Rightarrow \frac{(x-30)(x-40)}{x-35}<0$

$\Rightarrow xϵ\{I,2,3,\cdots 29\}\cup \{36,37,38,39\}$

so number of favorable cases are $=29+4=33$

Hence the required probability $\frac{33}{150}=\frac{11}{50}$