Nebraska Lottery, odds of 1 in a million?

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Discussion Overview

The discussion revolves around the odds of the Nebraska Lottery's Pick 3 game drawing the same number consecutively, specifically addressing the claim that the odds of such an event are one in a million. Participants explore the mathematical implications of this claim and the nature of probability in lottery draws.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the claim of "one in a million" odds, suggesting that with a 3-digit number, the chance of guessing correctly is one in a thousand for each draw.
  • Another participant asserts that the odds of repeating the same number in two successive draws should be considered independent, thus leading to a different probability calculation after the first draw.
  • A participant mentions the frequency of draws, noting that with six draws a week, the expected number of times the same number might repeat in a year is approximately 0.313.
  • There is a suggestion that the odds might be misrepresented if not specified in advance of the two drawings.
  • One participant humorously remarks on the perceived value of winning a small prize in the context of a supposedly rare event.

Areas of Agreement / Disagreement

Participants express differing views on the calculation of odds and the interpretation of the lottery's rules. There is no consensus on the correct probability or the implications of the "one in a million" claim.

Contextual Notes

The discussion highlights potential misunderstandings regarding the independence of draws and the assumptions underlying probability calculations. Specific definitions of terms and conditions of the lottery game may influence the interpretations presented.

robert Ihnot
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http://www.msnbc.msn.com/id/28802581/

Headline says: "Neb lottery draws same numbers twice in a row. The odds of such an occurrence? One is a million.

To begin with it was not the lottery, it was the pick 3, the number being 196. One in a million?
 
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If you have a 3-digit number to guess, you have one chance in a thousand of nailing it. What are the chances that you will be successful on a successive draw using ANY numbers (not just the same numbers)?
 
Clearly they are using base 100.
 
robert Ihnot said:
http://www.msnbc.msn.com/id/28802581/

Headline says: "Neb lottery draws same numbers twice in a row. The odds of such an occurrence? One is a million.

To begin with it was not the lottery, it was the pick 3, the number being 196. One in a million?

Heh. The three people who won that whopping $600 must be feeling a little short changed. After all, it was a one-in-a-million event, right? :smile: We live in a magical world.
 
1 in a million if specified in advance of the two drawings; the usual 1 in 1000 after the first pick since they're independent
 
There are six draws a week: Nebraska Pick 3, and thus 312 to 314 drawings per year (average 313.04..., call it 313). The expected number of times in a given year that a drawing repeats the previous one is 0.313. The chance that it happens in a given decade is 1 - .999^3130 = 95.6...%.
 

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