Lottery - Probability Discrepancy Comparing probabilities for the two national Canadian lotteries - Lotto 6/49 and Lotto Max, I have noticed something illogical:
First, you will see that the 2/6 + Bonus has a 1 in 81.2 chance. Meanwhile, 3/6 has a 1 in 56.7 chance. Isn't 3 out of 6 or 2 + Bonus out of 6 the same thing in the end as you matched 3 numbers out of 49 in both cases?
And second, if the 6/49 lottery is compared to the Lotto Max lottery (7/50), shouldn't there be a similar discrepancy in probabilities between the 3/7 + Bonus and 4/7 matches? Yet, for some reason they both have the exact same probability of 1 in 82.9. Why is that?
The probabilities for the 6/49 and Lotto Max lottery are located here:
http://www.wclc.com/games/lotto-649.htm
http://www.wclc.com/games/lotto-max.htm
Please help understand. Thank you!
 A: The key point is that the bonus drawing must be the last ball, while the non-bonus balls can be any of the first six balls that are drawn.
To illustrate why order matters, suppose you are watching the Lotto 6/49 drawing.  You have a ticket that has the numbers 01, 02, 03, 04, 05, 06, and you're assigned a bonus number 07.  The first two draws are 01 and 02.
At this point, are you more likely to match one of the balls 03, 04, 05, or 06 on one of the next four draws?  Or are you more likely to match 07 on one of the next four draws?
(This isn't a perfect analogy, since it deals with the conditional probability that you win if your first two draws are correct.  But it does illustrate why requiring the bonus ball to be a particular drawing makes a difference.)
I can't really explain why the payoffs are set as they are, though.  That may not be a mathematics question so much as a economics and psychology question (i.e., maybe it's a method of encouraging people to play more by giving them $10 payoffs more often.)
