Question

A number is chosen at random from 201 to 500. The probability that the chosen number is a multiple of 13 is

• A.
  $\frac{2}{25}$
• B.
  $\frac{1}{12}$
• C.
  $\frac{23}{300}$
• D.
  $\frac{11}{150}$

Answer 1

The correct option is C

$\frac{23}{300}$
Total numbers from 201 to 500 are 300.

Let A be the event of choosing the number between 201 and 500 such that it is a multiple of 13.

The numbers between 201 and 500 that are multiples of 13 are $208,221,234,\dots ,494.$

Now, these numbers form an AP with a = 208 and d = 13.

Also, last term, $l=a+(n–1)d\Rightarrow 494=208+(n–1)\times 13\Rightarrow 286=(n–1)\times 13\Rightarrow n=23$

$\therefore$ Number of outcomes favourable = 23


$P\left(A\right)=\frac{\text{Number of outcomes favourable to A}}{\text{Total number of outcomes}}=\frac{23}{300}$

Hence, the correct answer is option c.