A 3 digit natural number is selected at random .Find the probability that it is divisible by 2 but not by 3?
The numbers are between 100 and 999. There are 900 numbers to choose from.
450 of those numbers are divisible by 2. They are:
102, 104, 106, 108, ... 997, and 999
Of that group of 450 numbers, every third number is divisible by 3.
Thus, 150 numbers are divisible by 2 AND 3, and 300 numbers are divisible by 2 BUT NOT 3.
The probability of the latter situation is 300/900 = 1/3.