>
>Certainly this whole issue is a ripe one for some of that critical
>thinking stuff we talk about for our students.
>
>By the way, I am proud to say that, using all of my mathematical skills, I
>have NEVER lost in the lottery.
>
>Phil Mahler
>Middlesex CC
>Bedford, MA
>
Phil and others in the Great Lottery Debate:
If the lottery is of the 6/49 variety such as the one here in Canada, then
there are 49_C_6 = 13,983,816 combinations of which only one will be the
winner on any one play of the game. Thus if the prize is $1,000,000 and the
ticket costs $1, the mathematical expectation of the game is approximately
-$0.93; if the prize is $10,000,000 the expectation is about -$0.28. This
ignores all subsidiary prizes such as for any 5,4, or 3 numbers, so in fact
the expected loss will be considerably less than $0.93 and $0.28
respectively. Assignment question: determine the exected loss if the first
prize is $1,000,000, the prize for having any 5 numbers is $100,000, the
prize for any 4 numbers is $1,000, the prize for any 3 numbers is $10. Do
the relatively small expected losses per game "justify" playing the lottery? :)
Brian