## What are we learning ?

**Competency in Focus:** Probability of an event

This problem from American Mathematics Contest 8 (AMC 8, 2019) is based on calculation of probability of an event using the concept of divisibility. It is Question no. 13 of the AMC 8 2009 Problem series.## First look at the knowledge graph:-

## Next understand the problem

A three-digit integer contains one of each of the digits $1$, $3$, and $5$. What is the probability that the integer is divisible by $5$?
$\textbf{(A)}\ \frac{1}{6} \qquad \textbf{(B)}\ \frac{1}{3} \qquad \textbf{(C)}\ \frac{1}{2} \qquad \textbf{(D)}\ \frac{2}{3} \qquad \textbf{(E)}\ \frac{5}{6}$

##### Source of the problem

American Mathematical Contest 2009, AMC 8 Problem 13

##### Key Competency

### Finding probability of an event using the concept of divisibility

##### Difficulty Level

5/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics
Excursion Of Mathematics

## Start with hints

Do you really need a hint? Try it first!

First note that a number is divisible by $5$ if the unit digit is $5$ or $0$

Can you find all the three digit numbers that can be made using the digits given

So the three digit numbers are $135,153,351,315,513,531$.
among these only two numbers are divisible by $5$

Probability of an event = $\frac{\textbf{Number points supporting the event}}{Total number of outcomes}$
Ans=$\frac{\textbf{Number of 3 digit numbers divisible by 5}}{\textbf{Number of 3 digits number can be made}}=\frac{2}{6}=\frac{1}{3}$

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