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Lottery Probabilities

  1. Mar 28, 2010 #1

    I've had a question bugging me for a while and I've finally decided to seek an answer.

    Suppose you have a lottery game where one selects 6 numbers from 1 through 53. If you select the 6 winning numbers you win, regardless of the order. So our probability of winning is 53 C 6 = 53!/6!(53-6)!, or 1/22,957,480.

    Now suppose that some set T was the winning combination yesterday and you are considering playing the same set today. Intuitively, it would be difficult to imagine the same winning numbers appearing twice in a row (historically it hasn't happened in any lottery game with similar probabilities), yet, being that they are independent trials, the probability is equal.

    Is one equally as likely to win the lottery by playing yesterdays winning numbers than by choosing some other combination? It would seem to me that the probability of seeing the same combination win twice in a row is much less than to have different winning combinations.

    Please enlighten me.

    D Sputnik
  2. jcsd
  3. Mar 28, 2010 #2


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    True, because the probability of getting the same combination twice in a row is the square of getting the combination once. However once a combination comes up, the next drawing is independent, so getting that combination again is as likely as any other combination.
  4. Mar 28, 2010 #3


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    The odds are obviously far greater that today's numbers will not be the same as yesterday's numbers rather than getting the same numbers again. However, that's not your choice. You have to specify which of the different sets of numbers to pick, and there happen to be a LOT of those.

    Suppose yesterday's numbers were 1,2,3,4,5,6. The odds of seeing 1,2,3,4,5,6 twice in a row is very small (1/22,957,480 squared to be precise), but what are the odds of seeing 1,2,3,4,5,6 one day, and then the next day seeing 2,12,22,32,42,52? Just as low.
  5. Mar 30, 2010 #4
    Just to formalize what Mathman and Shredder said (to review my prob. knowledge,

    given that both answers were complete.)

    If the 5 numbers are selected at random, then, as you said, there are

    22,957,480 tickets, only one of which is the winning one. By def. of

    randomness ( I think the actual definition of randomness in the discrete

    case is that each outcome in the process is equally likely, but I am not

    100% on that.) . Then each of the 22957480 outcomes today can be paired up

    with 22957480 tomorrow, for a total of (22957480)^2 possible outcomes in two

    days. And out of those (22957480)^2 outcomes ( of the form (5-ple#1,5-ple#2))

    , only one will be a repeat.

    But, as Shreder said, the event : getting different combinations in 2 days

    has high probability.
  6. Mar 31, 2010 #5


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    No. There are 22957480 possibilities of repeats out of (22957480)^2 outcomes.
  7. Apr 2, 2010 #6
    "No. There are 22957480 possibilities of repeats out of (22957480)^2 outcomes. "

    I meant for a specific value, e.g., for the winning combination, there is only

    one way in which the same winning numbers --or any other _fixed_ numbers--

    can come out twice consecutively.

    And the probability of a repeat is --assuming random selection -- 1 in 22957480.
  8. Apr 2, 2010 #7
  9. Oct 9, 2011 #8
    A lottery is a form of gambling which involves the drawing of lots for a prize.Lottery is outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments. At the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in many countries, including the U.S.A. and most of Europe. This remained so until after World War II. In the 1960s casinos and lotteries began to appear throughout the world as a means to raise revenue in addition to taxes.

    Last edited by a moderator: Apr 26, 2017
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