Asked by Anonymous
A 3 digit natural number is selected at random .Find the probability that it is divisible by 2 but not by 3?
Answers
Answered by
drwls
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.
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.
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