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What are the odds?

Topic closed. 3 replies. Last post 12 years ago by johnph77.

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Redmond WA
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Posted: April 9, 2005, 12:56 pm - IP Logged

 

 What are the odds that all 6 numbers would be odd in Mega Millions?

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    Greenwich, CT
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    Posted: April 9, 2005, 1:08 pm - IP Logged

    The odds of having all six numbers be all-odd or all-even are 79:1.  1.27%

    All odd is half of that: 158:1 or 0.633%

    All-odd should happen an avg of two times in three years for MM.  Given that it just happened in November and yesterday....I wouldn't bet on it soon?!

      Maverick's avatar - yinyang
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      Posted: April 9, 2005, 2:23 pm - IP Logged
      Quote: Originally posted by MPJO on April 9, 2005


      What are the odds that all 6 numbers would be odd in Mega Millions?




      That happened 21 X before. Past statistics show the next draw to be an O/E of 3/2 or 2/3.

        johnph77's avatar - avatar
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        Posted: April 9, 2005, 4:18 pm - IP Logged

        JAG331 -

        Math is right, conclusions are in error.

        In a 52 ball pool there are 26 odd numbers and 26 even numbers. Odds of drawing an odd-numbered ball are 1::2.00.

        There are 51 balls left, 25 odd, 26 even. Odds of drawing an odd-numbered ball are 25::51, or 1::2.04. Cumulative odds, those of drawing two odd-numbered balls from 52, are 1::4.08.

        There are 50 balls left, 24 odd, 26 even. Odds of drawing an odd-numbered ball are 24::50, or 1::2.08. Cumulative odds, those of drawing three odd-numbered balls from 52, are 1::8.50.

        There are 49 balls left, 23 odd, 26 even. Odds of drawing an odd-numbered ball are 23::49, or 1::2.13. Cumulative odds, those of drawing four odd-numbered balls from 52, are 1::18.11.

        There are 48 balls left, 22 odd, 26 even. Odds of drawing an odd-numbered ball are 22::48, or 1::2.18. Cumulative odds, those of drawing five odd-numbered balls from 52, are 1::39.51.

        Then, one ball is drawn from a separate pool of 52. Odds of drawing an odd-numbered ball are 26::52 or 1::2.00. Multiplying these odds together gives you a chance of drawing all odd (or all even) numbers at 1::79.02.

        The proof is from another direction. If only odd numbers from 1 to 52 are considered, there are 26 numbers. If you were to have a 5/26 lottery matrix there would be 65,780 possibilities. In a 5/52 lottery matrix there are 2,598,960 possibilities. Dividing 2,598,960 by 65,780 gives you odds of drawing any 26 given numbers in a 5/52 lottery matrix, whether all odd, all even, 26 and under or 27 and over, of 1::39.51. Multiplying that by the 1::2.00 bonus ball odds yields game odds of 1::79.01.

        gl

        j

        Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

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