My company has a Safety Bingo game. For every day there is no accident in the plant, we pull a number. Every associate has a card and there are 110 cards in the game. The cards are the standard 5 column bingo cards, 15 possible numbers in each column, 75 numbers in total, with a free space in the middle. The pot is now $1,000. We had a winner on 8/8 so we cleared all of the cards. Usually it takes 19 - 25 days before we get a winner. However, only 6 days later, we had another winner!

I'd like to know what is the probability that we would get a winner (4 across plus the free spot) in only 6 days? Anybody know how to figure this out?

Buck,

interesting problem!

let me take a shot at this one: consider one card which has four numbers that must be matched along with the free spot to make a winner. this is a hypergeometric probability where we are drawing 6 numbers and matching four of them. the probablility of matching four numbers whit one card in play would be .0000123, or about 1 in 100,000 games this should happen.

now since you have 110 cards in play the probability of SOMEONE matching four numbers after six have been drawn would be 110 x .0000123, or .00135.

so for someone to win after only six days is about a 1 in 740 shot!

not really likely, but not as tough as winning the lotto

cheers
jerry

I thought i should add a comment that this is the probability of a bingo happening in the exact way that you stated.

the probability that ANY bingo would happen in 6 or fewer numbers is somewhat higher at ~0.000052. this link has some good info on bingo:

http://www.durangobill.com/BingoStats.html

Jerry