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# A number is randomly selected from the first 20 positive integers. What is the probability that it is divisible by 2, 3 or 4? Express your a

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A number is randomly selected from the first 20 positive integers. What is the probability that it is divisible by 2, 3 or 4? Express your answer as a common fraction.

Aug 1, 2017

#1
+2298
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To figure this problem out, let's first take a look at all the natural numbers up to 20.

The question asks for the probability for a number to be divisible by 2, 3, or 4. However, 2 is a factor of 4, so any number divisible by 4 is already divisible by 4, so there is no need to ever check for divisibility by 2. Also, if you prove a number is divisible by 2, you do not need to check if a number is divisible by 3.Let's take a look:

 Natural Numbers from 1-20 Divisible by 2? Divisible by 3? 1 2 ✔ 3 ✔ 4 ✔ 5 6 ✔ ✔ 7 8 ✔ 9 ✔ 10 ✔ 11 12 ✔ ✔ 13 14 ✔ 15 ✔ 16 ✔ 17 18 ✔ ✔ 19 20 ✔

Now, let's count how many numbers are divisible by either 2 or 3. There are 13 numbers that divisible by either 2 or 3.

Therefore, there is a $$\frac{13}{20}$$ chance that a number selected at random from the natural numbers 1 to 20 is divisible by either 2 or 3.

Aug 1, 2017
edited by TheXSquaredFactor  Aug 1, 2017

#1
+2298
+1

To figure this problem out, let's first take a look at all the natural numbers up to 20.

The question asks for the probability for a number to be divisible by 2, 3, or 4. However, 2 is a factor of 4, so any number divisible by 4 is already divisible by 4, so there is no need to ever check for divisibility by 2. Also, if you prove a number is divisible by 2, you do not need to check if a number is divisible by 3.Let's take a look:

 Natural Numbers from 1-20 Divisible by 2? Divisible by 3? 1 2 ✔ 3 ✔ 4 ✔ 5 6 ✔ ✔ 7 8 ✔ 9 ✔ 10 ✔ 11 12 ✔ ✔ 13 14 ✔ 15 ✔ 16 ✔ 17 18 ✔ ✔ 19 20 ✔

Now, let's count how many numbers are divisible by either 2 or 3. There are 13 numbers that divisible by either 2 or 3.

Therefore, there is a $$\frac{13}{20}$$ chance that a number selected at random from the natural numbers 1 to 20 is divisible by either 2 or 3.

TheXSquaredFactor Aug 1, 2017
edited by TheXSquaredFactor  Aug 1, 2017