Intuitive odds
February 25, 2015 10:28 AM   Subscribe

What are some examples that can help confused beginner-level students better understand what odds are and what they can tell us?

My students do not play the ponies, and examples relevant to sports betting are not clicking. I have run through my litany of technical and semi-technical explanations.
posted by palindromic to Education (12 answers total) 4 users marked this as a favorite
 
Drop chances in World of Warcraft?
posted by Johnny Assay at 10:34 AM on February 25, 2015


Where are you running into trouble? I feel like everyone has some good intuitions about coin flips and lottery tickets, but maybe these kinds of cases don't demonstrate the concepts you need. How about poker odds?
posted by grobstein at 10:37 AM on February 25, 2015


Dice rolls? That plus coin flips, card games, and lottery tickets were what my excellent introduction to probability theory instructor used last fall. He did a really good job, but he stuck almost exclusively to those examples--and when he brought in stuff he didn't expect us to know super well (like horse racing), he explained the rules before he asked us what we thought the answer would be.
posted by sciatrix at 10:39 AM on February 25, 2015 [1 favorite]


Roulette is a great game for this purpose. The rules are simple, it's easy to calculate the odds, and you can demonstrate how useful it is to be able to calculate odds by showing how much edge the house has given itself. Different combination plays and considering whether there's a 0, a 00 or a 000 give some nice problems to work through. After you've done roulette, you can do craps, whose rules are only slightly more complicated. It's fun to prove that both pass and don't pass are losing propositions, even though they're opposite bets, because the house won't pay on don't pass if a 12 turns up.
posted by ubiquity at 10:47 AM on February 25, 2015


Have you discussed the "birthday paradox"?
posted by Flexagon at 11:12 AM on February 25, 2015


Coin flips and Dungeon & Dragon dice (4 sided, 6-8-10-12) both in singles and in pairs (e.g. likelyhood of getting 7 with two six sided dice) seems pretty straightforward.
posted by furtive at 11:13 AM on February 25, 2015


I like to introduce probability with the "River Crossing" game -- it can be played on paper or with counters. Two versions are here, or you can take these and put your own spin on it. (p.s. advanced: write a program to simulate the game and see what the optimum strategy is!)
http://katm.org/wp/wp-content/uploads/2011/07/TheRiverCrossing.pdf
http://nzmaths.co.nz/resource/across-river
posted by Wulfhere at 12:32 PM on February 25, 2015


The recent Monty Hall problem on the blue?
posted by TWinbrook8 at 1:25 PM on February 25, 2015


Odds in daily life? What are the odds you have to stop at a stop light? Of having pancakes for breakfast? Of getting a particular toy in a Happy Meal? That it will snow in a Monday?

Odds for making decisions? If you want to buy a particular thing, will you go to a store if there is a 50% chance that the have it? 25%? 75%?
posted by SemiSalt at 1:34 PM on February 25, 2015


How about some basic daily decisions like:
Do you carry an umbrella with you to work?
When are extended warranties worth the money?
How many extra light bulbs do you need in the house?
posted by cross_impact at 1:41 PM on February 25, 2015


Are you looking for a context or an explanation? I haven't taught statistics, so my explanations won't be that polished. However, I can suggest a context. Do many of them play gem-sliding games like Bejeweled or Doctor Who Legacy or Kwazy Cupcakes? If you have, say, six different colors of gems and you have an equal chance of getting each one, what how likely is it that you will have a blue gem in the top right corner? How likely is it you will have another blue one either right below it or to its right? How likely is it that you will get 2 blue gems anywhere on the top row? Which is more likely on a row of 6 gems, getting one blue gem on each end or getting two right in the middle?
posted by Fanghorn Dungeon, LLC at 2:53 PM on February 25, 2015


There is a boardgame called Can't Stop which is heavily based on the odds of rolling the numbers 2 through 12 using 2 regular dice.

Other examples you can build/use:

If you buy 10 pairs of black socks and 5 pairs of white socks and put them all individually in a drawer and then close your eyes to draw one out, what are the odds that it will be black?

Get a CandyLand board game. Count each color of card in the deck. As you play the game, what are the odds that you will draw a given color?

Translate that to Blackjack - given that there are a lot of cards whose value is 10, what are the odds of getting a 10 on each draw?

For each of the above, keep in mind that as you repeat each experiment, the number of each instance changes, so the odds change. You can calculate the odds at each play, or every 5 plays, or whatever, as long as you keep track of the value of each draw.


Other activities/samples:
Here's some more examples of probability in real life.

This is an interesting worksheet with a lot of examples. I like exercise 5.9 to help your students see when probabilities are stated incorrectly.
posted by CathyG at 3:14 PM on February 25, 2015


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