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  1. #1
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    Statistical Question (2000 SR1)

    Assuming a population which is entirely random numbers, which of the following assumptions would be "more" correct?

    1. That the most frequently occurring numbers would occur next, or...

    2. The least frequently occurring numbers would occur next since they have not occurred very often.

    Thanks,

  2. #2
    Uranium Lounger
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    Re: Statistical Question (2000 SR1)

    Neither. If the numbers are random, then every possible number has the same probability of comming up next, no matter what has happened before.
    Legare Coleman

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    Re: Statistical Question (2000 SR1)

    Even if the population is finite?

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    Re: Statistical Question (2000 SR1)

    I agree with Legare - any number.
    I think it is a matter of separating Possibility and Probability.

    Take flipping a coin. You have two Possibilities - heads and tails.
    If you fip and get heads, the Probability is the next flip will produce tails as the overall odds are 50:50 and statistically you can expect an even spread.
    However, the Possibility is that it will be either, as each flip has an equal chance of producing a head or a tail.

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    Re: Statistical Question (2000 SR1)

    If the selection process is random, it does not matter if the population is finite. On any selection, the population is always finite - the current population plus one.
    Legare Coleman

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    Re: Statistical Question (2000 SR1)

    If the sample is finite, then there may well be a difference.

    For instaance, if, in a pack of cards, 12 hearts have been drawn (12 cards out of 52, leaving 40 cards), then the chance of the next card drawn being a heart is 1 out of 40 (vs 1 out of 4 of the first card drawn being a heart).

    But the population must be very finite for this to happen.
    Subway Belconnen- home of the Signboard to make you smile. Get (almost) daily updates- follow SubwayBelconnen on Twitter.

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    Re: Statistical Question (2000 SR1)

    After reading Geoff's response, I think I may have misunderstood this reply. If by finite population, you are refering to the population from which the numbers are chosen, then the results are not truly random, and I agree with Geoff's response.
    Legare Coleman

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    Re: Statistical Question (2000 SR1)

    Hi:
    When sampling, without replacement, from a finite population, that originally had an equal distribution of elements at each value, then your second premise would be true: "the least frequently occurring numbers would " have the the higher probability of showing up on the next draw.occur next since they have not occurred very often.



    was formed by a random process such that all values had an equal chance of being included to the same degree, then

  9. #9
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    Re: Statistical Question (2000 SR1)

    Legare,

    I think there's a misconception out there- common amongst gamblers.

    "If I've thrown 20 heads in a row- what's the chance of heads being the next throw"

    "Mr Jones has had 6 children- all boys. What's the chance of the next child being a boy?"

    "This poker machine has not paid for the last xx. So it must be due for a payout now".

    I'm not sure if that is behind the original question.

    The probability of any random event occuring is completely independent of any previously occurring random even. As long as both events truly are random.

    We're getting way out of scope of an Excel forum. I guess that Excel just attracts the interest of statisticians and gamblers <img src=/S/smile.gif border=0 alt=smile width=15 height=15>
    Subway Belconnen- home of the Signboard to make you smile. Get (almost) daily updates- follow SubwayBelconnen on Twitter.

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    Re: Statistical Question (2000 SR1)

    A clarification would help -- once a number is selected from the population, does the size of the population left to be selected from decrease? Or, does the number get tossed back into the hat possibly to be drawn again?

    If a selected number is not put back, its frequency within the pool will be decreased, increasing the probability that any other number will be selected next. If the number is returned to the pool, it has the potential for being drawn again, and none of your initial probabilities will have changed.

    Even if selected completely at random, a number that occurs more frequently within your population will always have a greater chance of being selected. A rare number may never be selected, or it may always be selected; a common number may never be selected, or it may always be selected. Probability dictates that a rare number is more likely not to be selected, and a common number will be.

    Hmmm... I think my stats prof would be proud -- something sunk in! <img src=/S/rofl.gif border=0 alt=rofl width=15 height=15>

  11. #11
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    Re: Statistical Question (2000 SR1)

    <hr>something sunk in<hr>
    Do you really sink so?
    Subway Belconnen- home of the Signboard to make you smile. Get (almost) daily updates- follow SubwayBelconnen on Twitter.

  12. #12
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    Thanks All!

    Thanks for everyone's input.

  13. #13
    Uranium Lounger
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    Re: Statistical Question (2000 SR1)

    I typically see this kind of question from someone trying to create a spreadsheet that will predict lotto numbers given a list of previous numbers.
    Legare Coleman

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    Re: Statistical Question (2000 SR1)

    U got the prize! Actually I was trying to dislodge a conviction by a coworker that the numbers which are drawn most frequently are more likely to be drawn next. She has some interesting data, but I think to be mostly coincidental.

    Thanks,

  15. #15
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    Re: Statistical Question (2000 SR1)

    Then, there are some things that you can say about the probability of a number comming up:

    1- There is no change in the probability of a number comming up based on numbres from previous drawings. If the number 1234 has hit every day for the last week, it still has the same probability of hitting today that it did one week ago.

    2- Depending on how the numbers are drawn, there may be a difference in the probability of certain numbers in the set of all possible numbers. For example, if the ping pong ball machine is used where each digit drawn is not replaced before the next digit is drawn, then the probability 4444 being drawn is less than the probability of 1444 which is less than 1244 which is less than 1234.
    Legare Coleman

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