Question

A two-digit number from $10$ to $99$, inclusive, is chosen at random. What is the probability that this number is divisible by $5$?

• A. $\frac{1}{5}$
• B. $\frac{2}{9}$
• C. $\frac{19}{90}$
• D. $\frac{18}{19}$
• E. $\frac{19}{91}$

Answer 1

The correct option is A $\frac{1}{5}$

A two digit number from $10$ to $99$ inclusive is chosen at random.

$90$ numbers exist in the range from $10$ to $99$.

Therefore, the total outcomes is $90$.

$18$ of them are divisible by $5$.

Therefore, possible outcomes is $18$.

Hence, the probability that the chosen number is divisible by $5$ is

$\text{probability}=\frac{\text{possible outcomes}}{\text{total outcomes}}$

$=\frac{18}{90}=\frac{1}{5}$

Hence, the probability that the chosen number is divisible by $5$ is $\frac{1}{5}$.

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