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

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    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.

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