Question

A three digit number was chosen at random. Find the probability that it is divisible by both 2 and 3

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{9}$
• D. $\frac{1}{8}$

Answer 1

The correct option is B $\frac{1}{6}$

For a $3$ digit no. to be divisible by both $2$ and $3$ it should be divisible by $6$

No. of $3$ digit no.s divisible by $6=\left|\frac{999}{6}\right|$

$=166-16$

$=150$

No. of $3$ digit no.s$=900$

Probability of selecting a no. which is divisible by $6=\frac{150}{900}=\frac{1}{6}$