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!

JL.....