# Category Archives: probability

## Roll Up the Rim Wrap Up

Well, it appears that we beat the odds this year when it comes to Rolling Up the Rim to Win.  By “we”, I mean the lucky friends of mine.  Not only are they lucky to have me as a friend, who brings them coffee unexpectedly, they also benefitted by winning rims.  Out of the 7 coffees/hot beverages I purchased to give to someone else, 3 cups turned out to be winners.  (And in case you were wondering, YES, I do give winning rims…I do not expect to have the prize back.  My rule is, if the prize is less than \$1000, then that’s fine.  If it’s \$1000 or more, we’ll split it.  There.  It’s in writing for any future instances and legal battles.  What’s your personal rule when it comes to winning rims on beverages you bought/gifted?  Leave your rule by posting a comment below.)

Overall, our win totals were better than the posted odds.  Now, honestly, we didn’t track this meticulously, as some beverages I bought for others, I didn’t follow up on whether or not they were winners.  I figured people would tell me if they did win.  Which is to say, maybe there were more losing cups than we kept track of.  Also, one might say being altruistic leads to a greater winning percentage for the receivers of charity, but then again, isn’t the charitable act a win in of itself?  One could speculate forever about this, which is the fun of mathematical inquiry and the field of probability and statistics.

Here are the final totals for Spring 2012.  This year, Tim Horton’s (I refuse to use the public relations and media friendly moniker “Tim Hortons” as it pays little respect to the founder of Tim Horton’s and separates the chain’s history from the man that started it all, hence, Tim Horton’s–or the coffee shop belonging to Tim Horton) claims that the odds are 1 in 6. Let’s see about that one…

Drinks for me: 14
Drinks for others: 7
Drinks for me, purchased by others: 2 (Nya:weh, Mr. Sowden)

Total Drinks Purchased: 23

Winning cups for me: 2
Winning cups for others: 3
Winning cups for me, purchased by others: 0

Total Winning Cups: 5

Odds for me: 2 in 14
Odds for others: 3 in 7
Odds for me, purchased by others: 0 for 2

Total odds: 5 in 23.

That’s certainly better than 1 in 6!  How about that for a deep math problem?  Sort these odds using 1 in 6 as the midpoint, where some odds are better and others are worse.  Or seeing as it is Stanley Cup playoff time, track odds of winning the cup with actual results by round.

Consider tracking your own purchases but more importantly, discuss and utilize real life instances of probability to enable students to make real life connections to the math they are learning

## Roll Up MY Rim and Win!!

Well, it’s that time of year, once again.  For anyone who has read my blogs over time, you may remember my posts on the probability of winning on a Roll Up the Rim Tim Horton’s cup.  If not, check them out here and here.  Last year I thought to look at the odds and how well they matched up with my hot beverage purchases.  I used the breakdown below to score my results (last year’s end totals are displayed):

Drinks for me: 23
Drinks for others: 6
Drinks for me, purchased by others: 4

Total Drinks Purchased: 33

Winning cups for me: 2
Winning cups for others: 2
Winning cups for me, purchased by others: 0

Total winning cups: 4

Odds for me: 2 in 23
Odds for others: 2 in 6
Odds for me, purchased by others: 0 in 4

Total odds: 4 in 33

This year, Tim Horton’s (I refuse to use the public relations and media friendly moniker “Tim Hortons” as it pays little respect to the founder of Tim Horton’s and separates the chain’s history from the man that started it all, hence, Tim Horton’s–or the coffee shop belonging to Tim Horton) claims that the odds are 1 in 6.  Let’s see about that one…

Drinks for me (so far): 13
Drinks for others (so far): 7
Drinks for me, purchased by others: 1 (Nya:weh, Mr. Sowden)

Total Drinks Purchased: 21

Winning cups for me: 2
Winning cups for others: 3
Winning cups for me, purchased by others: 0

Total Winning Cups: 5

Odds for me: 2 in 13
Odds for others:  3 in 7
Odds for me, purchased by others:  0 for 1

Total odds:  5 in 21.

Consider tracking your own purchases but more importantly, discuss and utilize real life instances of probability to enable students to make real life connections to the math they are learning.

## What are the odds?

If you read this blog regularly, you may remember my probability post concerning the roll up the rim to win Tim Horton’s cups. At the time i posted it, i was running at a winning cup every two drink purchases. Since then, i haven’t seen a single winner in 13 cups (unlucky??). At first glance, it would seem that i have had a run of bad luck. But when you look closely at the numbers, and compare them to the stated odds of Tim Horton’s winning cups (1 in 6 this year), it would seem that i could have easily anticipated my string of ‘bad luck’.

Right now i sit at 2 wins out of 17 cups. Taking the 1 in 6 odds that Tim Horton’s advertises, one might think my next purchase should very well be a winning cup. 1 in 6 odds would mean 3 wins for every 18 cups purchased. However, by that logic, could i potentially not see a winning cup until the 23rd cup purchased, followed by a second win in a row at cup number 24??? This would still give me 1 in 6 odds, should the 23rd and 24th cup prove to be winners.
So next time you think you’ve hit a run of bad luck, or a jackpot of multiple winners, remember the math behind it all, and that the odds were right there in front of you the entire time.

## Roll up the Probability Possibilities

A couple of years ago i posted a running total of my roll up the rim to win coffee purchases. i wanted to see if the 1 in 9 chance would actually occur in my own purchases, while also being aware of the geographical inconsistencies in which Tim Hortons distributes its winning cups. This allowed my students and i to engage in conversations around a real-life example of probability. It was fun, (and it may actually resulted in a few coffees being purchased FOR me by some students and their parents — wink, wink.) So i will continue this practice on the Six Nations Numeracy blog this year. Tim Hortons claims a 1 in 6 chance of winning this year, as they have added more prizes.

However, one factor i didn’t anticipate that may have “skewed” the results, were those instances where i actually purchased the coffee, but as a gift for someone else. Did those winning cups count towards my total? Is that why my actual buying experience didn’t concur with Tim Hortons’ alleged odds? So this year, i will include any winning cups i bought for others. Maybe good karma has its way of working and messing with probability?
Drinks for me: 23
Drinks for others: 6
Drinks for me, purchased by others: 4
Total Drinks Purchased: 33
Winning cups for me: 2
Winning cups for others: 2
Winning cups for me, purchased by others: 0
Total winning cups: 4
Odds for me: 2 in 23
Odds for others: 2 in 6
Odds for me, purchased by others: 0 in 4
Total odds: 4 in 33