Question

An integer is chosen between $1$ and $100$. What is the probability that it is not divisible by $9$?

• A. $\frac{10}{100}$
• B. $\frac{11}{100}$
• C. $\frac{89}{100}$
• D. $\frac{90}{100}$

Answer 1

The correct option is C $\frac{89}{100}$

A no is chosen between $1$ and $100$

$n\left(s\right)=100$

$n\left(E\right)=n\left(s\right)-n\left(\overline{E}\right)$

$n\left(\overline{E}\right)=$ no divisible by $9=\left|\frac{100}{9}\right|=11$

$=n\left(E\right)=100-11$

$n\left(E\right)=89$

$p\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}=\frac{89}{100}$.