First slide

Theorems of probability

Question

$A natural number is chosen at random from the first 100 natural numbers. The probability that x + \frac{100}{x} > 50 is$

Moderate

A

$1 / 10$
B

$11 / 50$
C

$11 / 20$
D

$None of these$

Solution

We have,
$\begin{array}{l} x + \frac{100}{x} > 50 \\ or x^{2} + 100 > 50 x \\ or (x - 25)^{2} > 525 \\ \Rightarrow x - 25 < \sqrt{525} or x - 25 > \sqrt{525} \\ \Rightarrow x < 25 - \sqrt{525} or 25 + \sqrt{525} \end{array}$
$As x is a positive integer and \sqrt{525} = 22.91, we must have$
$x \leq 2 or x \geq 48 . Thus, the favorable number of cases is 2 + 53 = = 55$
$Hence, the required probability is 55 / 100 = 11 / 20 .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App