Question

Out of the numbers $1$ to $150$, one is to be selected at random. The probability that the number selected is perfectly divisible by $15$ is.....

• A. $\frac{2}{18}$
• B. $\frac{1}{15}$
• C. $\frac{27}{128}$
• D. $\frac{7}{128}$

Answer 1

Answer: (B)

$\frac{1}{15}$

Total numbers are $n\left(S\right)=150$

Numbers divisible by $15$ from $1$ to $150$ are $\{15,30,45,60,75,90,105,120,135,150\}$

$n\left(E\right)=10$

Hence the probability that the number selected is perfectly divisible by $15$ is $\frac{n\left(E\right)}{n\left(S\right)}=\frac{10}{150}=\frac{1}{15}$