# 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 $3 = \frac{300}{900}$

$= \frac{1}{3}$

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