Chance News 35
We (Laurie Snell) were not able to find any evidence that this really appeared in USA Today.
Our first item was suggested by Fred Hoppe at MacMaster University who's research is in probability and statistics with a hobby of lottery problems.
In this lottery it was better to win third than second place
The Lotto 6/49 in Ontario Canada asks you to choose six numbers from 1 to 49 on up to 10 boards (each board costs $2) or ask for a Quick Pick and the lottery terminal will randomly select your numbers. The Lotto officials randomly draw 6 numbers from 1 to 49 and a bonus number from 1 to 49. The payoffs are
47% of LOTTO 6/49 draw sales is dedicated to the Prize Fund. The total amount of $5 and $10 prizes are paid from the Prize Fund and the balance of the fund (the Pools Fund) is then allocated between the 4/6, 5/6, 5/6 + Bonus and 6/6 prize categories as indicated in the table above. Any amount not won in the 6/6 or 5/6 + Bonus prize categories is added to the 6/6 Jackpot prize for the next draw.
In the March 19, 2008 Lotto 6/49 numbers drawn were 23 - 40 - 41 - 42 - 44 - 45 and the bonus was 43.
Can you imagine the consternation of the poor folks who, against the odds, matched 5/6 numbers and the bonus number, then found their excitement turned to dismay upon learning their share was only $1,193.70 because of the 239 who matched likewise. The third place winners (match 5/6 only) each took home $2,223.40.
Fred suggested that we could determine the probability that there will be more third place winners than second place winners assuming quickpicks. What additional information would you need and given this how would you compute this probability?