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10 September, 17:22

onsider a random number generator designed for equally likely outcomes. If numbers between 0 and 99 are chosen, determine which of the following is not correct. a. If 100 numbers are generated comma each integer between 0 and 99 must occur exactly once. b. For each random number generated comma each integer between 0 and 99 has probability 0.01 of being selected. c. If a very large number of random numbers are generated comma then each integer between 0 and 99 would occur close to 1 % of the time. d. The cumulative proportion of times that a 0 is generated tends to get closer to 0.01 as the number of random numbers generated gets larger and larger.

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  1. 10 September, 19:19
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    The following option is not correct:

    (a) If 100 numbers are generated comma each integer between 0 and 99 must occur exactly once.

    Step-by-step explanation:

    This is not correct, as there is a possibility of an integer being generated twice when 100 numbers are generated.

    This can be explained with an example such as stated below:

    3 numbers are to be generated.

    The number generated can either be 1, 2, or 3.

    The probability for all three numbers to be generated once when the generator is run 3 times is:

    (1/3) * (1/3) * (1/3) * Number of ways to arrange the three numbers

    Thus this probability will be:

    Probability = (1/3) ^3 * 3!

    Probability = 0.222

    Since the probability here is not equal to 1, the probability for the same thing happening at a larger scale will also not be 1.
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