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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
United States
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July 29, 2004
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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?

Greenwich, CT
United States
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May 24, 2004
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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?!

USA
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October 29, 2004
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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.

CA
United States
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December 10, 2003
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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.....

Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

=^.^=

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