Question

If a number $n$ is chosen at random from the set $\left\{11,12,13,.........,30\right\}$. Then, the probability that $n$ is neither divisible by $3$ nor divisible by $5$, is

• A. $\frac{7}{20}$
• B. $\frac{9}{20}$
• C. $\frac{11}{20}$
• D. $\frac{13}{20}$

Answer 1

The correct option is C

$\frac{11}{20}$

Finding the probability:

Given, Total outcome is $\left\{11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30\right\}=20$

Favorable outcome means, Number which is not divided by $3\&5$ is $\left\{11,13,14,16,17,19,22,23,26,28,29\right\}=11$

Required probability $=\frac{\mathbf{F}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{u}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}\mathbf{=}\frac{\mathbf{11}}{\mathbf{20}}$

Hence, correct answer is option $\left(C\right)$.