Chance News 35

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USA Today has come out with a new survey: Apparently three out of four people make up 75 percent of the population.

David Letterman,

04/12/1947 -

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

Fred writes:

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.


What information would you have to have to estimate the probability that the third place winners would do better than the second place winners. Given this information how would you estimate the probabiity?