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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.

Guest Aug 1, 2017

Best Answer 

 #1
avatar+815 
+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 1-20Divisible 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
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1+0 Answers

 #1
avatar+815 
+1
Best Answer

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 1-20Divisible 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

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