Monday, April 19, 2010

Expect to See Repeated Pick 3 Numbers after 37 Drawings (Lottery Trivia Answer 2010-07)

Last Week's Trivia Question #2010-07 was: 
To win the Pick 3 State lottery games, a player must correctly predict the winning number in the range of 000 to 999. If this number correctly matches the one drawn, the player wins approximately $250 on a $0.50 bet. So, if you like to play this game, you have probably wondered:
  • How often would you expect to see numbers repeat?
  • Or, in other words, how big would given a subset of daily results need to be in order to see duplicate numbers?
To answer these questions, we must remember that there are 1000 different numbers.
  • Based entirely on an even distribution, the probability of any number being drawn is 1 in 1000.
  • This means that any one given number should repeat once every 1000 drawings on the average.
  • But, we all know that numbers repeat at various intervals.
  • Thus, we refer back to the "Birthday Question" to determine how large of a sample is required to observe duplicate numbers.
  • After solving this problem, we find that: in a set of approximately 37 drawings, we can be 50% confident that one of the numbers in that group will be a duplicate.
  • And, if we examine a results set of 118 drawings, we can be 99.9% confident that one of those numbers will be repeated!

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