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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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