Question

An integer is choosen from $\{2k/-9\le k\le 10\}$. The probability that it is divisible by both $4$ and $6$ is

• A. $\frac{1}{10}$
• B. $\frac{1}{20}$
• C. $\frac{1}{4}$
• D. $\frac{3}{20}$

Answer 1

The correct option is D $\frac{3}{20}$

Given, $S=\{-18,-16,-14,---,20\}$

Thus $n\left(S\right)=20$

$E=$ Divisible by $4$ and $6$ i.e integer is divisible by $12$
$=\{-12,0,12\}$
$n\left(E\right)=3$

Therefore, $P\left(E\right)=\frac{3}{20}$