Question

A two-digit number is formed with the digits $2,5$ and $7$, where repetition of digits is not allowed. Find the probability that the number so formed is divisible by $3$

Answer 1

The possible outcomes when a two-digit number is formed with the digits $2,5$ and $7$ are {$25,27,52,57,72,75$}. Therefore, the number of possible outcomes when a two-digit number is formed with the digits $2,5$ and $7$ is $6$.

Now, the possible outcome of a number divisible by $3$ is {$27,57,72,75$}, which means the number of favourable outcome is $4$.

Therefore, probability $P$ of a number divisible by $3$ is:

$P=\frac{4}{6}=\frac{2}{3}$

Hence, the probability of a number divisible by $3$ is $\frac{2}{3}$.