So I was given a question with two parts:

The first part is like this:

How many 3-digit integers (integers from 100 to 999 inclusive) are divisible by 5?

My solution: $\frac{(999-100+1)}{5} = 180$

The second part following the first part is like this:

What is the probability that a randomly chosen 3-digit integer is divisible by 5?

I saw a similar question where they took the above answer and subtracted by 17 and added 1

Is this correct?

Solution: $180/900$

  • $\begingroup$ Why are you subtracting by $17$ and adding $1$? $\endgroup$ – miradulo Jan 20 '16 at 14:59
  • $\begingroup$ @DonkeyKong In the previous example they did that i thought it was a general method, was unsure so i just took the first answer and did that $\endgroup$ – Zero Jan 20 '16 at 15:01
  • $\begingroup$ Something like "subtracting $17$ and adding $1$" is hardly ever going to be a general method. That's like saying hocus pocus at a math equation. You know how many 3 digits integers there are, and you now know how many of these 3 digit integers are divisible by 5. To get the probability for a randomly chosen 3 digit integer, just divide your result $180$ by your sample space of $900$. $\endgroup$ – miradulo Jan 20 '16 at 15:05
  • $\begingroup$ @DonkeyKong Thank you $\endgroup$ – Zero Jan 20 '16 at 15:07

Number of $3$ digit numbers which are divisible by $5$ :

To calculate this, note that there are $9$ choices for putting digits in the hundreds' place $[1-9]$, $10$ choices for putting digits in the tens' place $[0-9]$ and $2$ choices for putting digits in the units' place $[0,5]$. Hence total number of $3$ digit numbers which are divisible by $5$ is $9\times 10 \times 2 =180$.

However total number of $3$-digit numbers is $900$.

So the probability is $\large\frac{180}{900}=\frac{1}{5}$


Lowest 3 digit no is 100 highest 3 digit no is 999 so total 3 digit no=S_A/D+1 is a formula where s is last term an a is 1st term d is common difference as in this case 999 is last term and 100 is 1st term and 1 is common diffdrence =999_100÷1+1=900 Now series of 3 digit no divided by 5 100,105............995 No divisible by 5=995_100÷5+1=180 same formula used as above so probability=180÷900=1/5


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.