Activity : Ask all the students in your class to write a 3-digit number. Choose any student from the room 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 .
To do:
We have to find the probability that the number written by her/him is divisible by 3.
Solution:
The total number of students in the class $=30$
The probability of selecting a student $= \frac{30}{30}$
$= 1$
Three digit numbers are $100,101,.......999$
Total number of three digit numbers $= 999 - 100 +1 $
$= 900$
Multiples of 3 in three digit numbers $= 102,105 ….., 999$
Therefore,
Number of multiples of 3 in three digit numbers $= \frac{900}{3}$
$= 300$
The probability that the number written by her/him is divisible by $3 = \frac{300}{900}$
$= \frac{1}{3}$
Related Articles
- If a number is divisible by 3 it must be divisible by 9. (True/False)
- Find the greatest 3 digit number that is exactly divisible by 6 15 and 21
- Find the smallest value of a, if the number\(6a4231\) is divisible by 3.
- Sum of a two-digit number and the number obtained by reversing the digits is always divisible by?
- Given that the number $\overline{35a64}$ is divisible by 3, where $a$ is a digit, what are the possible values of $a$?
- Find the greatest 3 digit number which is divisible by the number 4 ,5 and 6.
- Which of the following statements are true?(i) If a number is divisible by 3, it must be divisible by 9.(ii) If a number is divisible by 9, it must be divisible by 3.(iii) If a number is divisible by 4, it must be divisible by 8.(iv) If a number is divisible by 8, it must be divisible by 4.(v) A number is divisible by 18, if it is divisible by both 3 and 6.(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.(viii) If a number divides three numbers exactly, it must divide their sum exactly.(ix) If two numbers are co-prime, at least one of them must be a prime number.(x) The sum of two consecutive odd numbers is always divisible by 4.
- If $x$ is a digit such that the number $\overline{18\times71}$ is divisible by 3, find possible values of $x$.
- A number is divisible by $12$. By what other numbers will that number be divisible?
- Determine the smallest 3-digit number which is exactly divisible by 6,8 and 12.
- Check if any permutation of a number is divisible by 3 and is Palindromic in Python
- 18 is divisible by both 2 and 3 . It is also divisible by \( 2 \times 3=6 \). Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by \( 4 \times 6=24 \) ? If not, give an example to justify your answer.
- If a number is divisible by 3 need it to be tested for 9? Justify your answer by stating any 2 numbers which are divisible by 3 but not by 9.
- Check if 74526 is divisible by 3.
- Largest number with the given set of N digits that is divisible by 2, 3 and 5 in C++
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies