Question

$\{2,4,6,8,10,12,14,16,18\}$
If a number is selected at random from the set above, calculate the probability of the number being divisible by $3$.

• A. $\frac{1}{3}$
• B. $\frac{4}{9}$
• C. $\frac{5}{9}$
• D. $\frac{2}{3}$
• E. $1$

Answer 1

Answer: (A)

$\frac{1}{3}$

Given numbers are $\{2,4,6,8,10,12,14,16,18\}$
Total given numbers $=9$
Numbers divisible by $3$ are $6,12,18$.
Number of numbers divisible by $3$ are $3$.
We know formula of probability is $\frac{\text{Favourable outcomes}}{\text{Total possible outcomes}}$.
So probability of the number being divisible by $3$ is $\frac{3}{9}=\frac{1}{3}$.