Question

A three digit number, which is multiple of $11$, is chosen at random. Probability that the number so chosen is also a multiple of $9$, is equal to

• A. $\frac{1}{9}$
• B. $\frac{2}{9}$
• C. $\frac{1}{100}$
• D. $\frac{9}{100}$

Answer 1

The correct option is A $\frac{1}{9}$

Three digit number divisible by $11$ will belong to $\{10\times 11,11\times 11,12\times 11,...,90\times 11\}=81$ number.
The number that is also divisible by $9$ will be $\{18\times 11,27\times 11,36\times 11,...,90\times 11\}=9$ numbers
$\Rightarrow n\left(S\right)=81$ and $n\left(E\right)=9$
$\therefore P\left(E\right)=\frac{1}{9}$