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Random number from a range: probability it is a multiple of some numbers (inclusion-exclusion)

This type of question, asked 3 times: 27 Jul 2022, 29 Jul 2022, 29 Jan 2024. All 3 questions below, oldest first.

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  1. Question 1

    27 Jul 2022

    74
    Let SS be the sample space of all five- digit numbers. If pp is the probability that a randomly selected number from SS, is a multiple of 7 but not divisible by 5, then 9p9p is equal to

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  2. Question 2

    29 Jul 2022

    79
    Let S={1,2,3,…,2022}\mathbf{S = \{ 1,2,3,\ldots,2022\}}. Then the probability, that a randomly chosen number nn from the set SS such that HCF(n,2022)=1HCF(n,2022) = 1, is:

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  3. Question 3

    29 Jan 2024

    169
    An integer is chosen at random from the integers 1 , 2,3,…,502,3,\ldots,50. The probability that the chosen integer is a multiple of atleast one of 4,6 and 7 is

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