Question

In a class of $40$ students, ask them to write a 3-digit number. Choose any student at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Answer 1

Total number of students in the class $=40$
and out of $40$ students, number divisible would be:

Case : Number divisible by $3$ or Sum of its digits divisible by $3$
Total $3$ digit numbers $=100$ to $999$
$=900$ numbers

First number divisible is greater than $100$, i.e., $=102$
Now add $3$ to $102$ till $999$
$a=102$ Common difference $d=3$
$n=?$ Last number $=999$

$\Rightarrow 999=a+(n-1)d$

$\Rightarrow 999=102+(n-1)3$

$\Rightarrow \frac{897}{3}=n-1,n=300$

Probability $=\frac{300}{900}=\frac{1}{3}$