Question

An integer is chosen form $\{2k /-9 \leq k \leq 10\}$. 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

Answer: (D)

Let $S=\{2 k \mid-9 \leq k \leq 10\}=$
$\{-18,-16,-14, \ldots, 0,2,4,6, \ldots 20\}$
Total number of possible outcomes $=20$
Favourable outcomes are $-12,0$ and 12
So, number of favourable outcomes $=3$
$\therefore $ Required probability $=\frac{3}{20}$