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    Question

    A number is randomly chosen from 1 to 100(both

    inclusive). What is the probability that it is divisible by 2, 3 or 5?
    A 71/100 Correct Answer Incorrect Answer
    B 37/50 Correct Answer Incorrect Answer
    C 14/25 Correct Answer Incorrect Answer
    D 17/25 Correct Answer Incorrect Answer

    Solution

    Total numbers divisible by 2 = 100/2 = 50
    Total numbers divisible by 3 = 100/3 = 33
    Total numbers divisible by 5 = 100/5 = 20
    Numbers that are multiples of 2 and 3, 3 and 5, 2 and 5 would have been added twice. So we need to subtract it.
    Total numbers divisible by 2 and 3 = 100/6 = 16
    Total numbers divisible by 3 and 5 = 100/15 = 6
    Total numbers divisible by 2 and 5 = 100/10 = 10
    We now need to add the number divisible by 2,3, and 5
    LCM = 2 x 3 x 5 = 30
    Total numbers divisible by 30 = 100/30 = 3
    So numbers divisible by 2,3 or 5 = 50 + 33 + 20 - (16 + 6 + 10) + 3 = 103 - 32 + 3 = 74
    Required probability = 74/100 = 37/50

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