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# Probability in Divisibility | AMC-10A, 2003 | Problem 15

Try this beautiful problem from Probability based on divisibility.

## Probability in Divisibility - AMC-10A, 2003- Problem 15

What is the probability that an integer in the set ${1,2,3,…,100}$ is divisible by $2$ and not divisible by $3$?

• $\frac {33}{100}$
• $\frac{1}{6}$
• $\frac{17}{50}$
• $\frac{1}{2}$
• $\frac{18}{25}$

### Key Concepts

Number system

Probability

divisibility

Answer: $\frac{17}{50}$

AMC-10A (2003) Problem 15

Pre College Mathematics

## Try with Hints

There are total number of integers are $100$.and numer of integers divisible by $2$ is $\frac{100}{2}$=$50$. Now we have to find out divisible by $2$ and not divisible by $3$. so at first we have to find out the find out the numbers of integers which are divisible by $2$ and $3$ both.......

can you finish the problem........

To be divisible by both $2$ and $3$, a number must be divisible by the lcm of $(2,3)=6$.

Therefore numbers of integers which are divisible by $6$=$\frac{100}{6}=16$ (between $1$ & $100$)

can you finish the problem........

Therefore the number of integers wcich are divisible by $2$ and not divisible by $3$= $50 - 16=34$.

So require probability= $\frac{34}{100}=\frac{17}{50}$

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