Tall Tales for Probability Class

Probability is fun.

Nothing drives me nuttier than boring probability units.  Endless worksheets filled with tales of balls in urns and cards being drawn from decks.  Nothing screams for fun and games more than a probability unit.  Here’s some ideas for you to try:

DRAW THE CUBES, WIN A JOLLY RANCHER!

This is a good opener for teaching dependent events.  Take a brown paper lunch bag, and place inside 20 colored cubes.  In the past, I have used 10 white, 6 red and 4 blue.  Do NOT let the students know what chips are in the bag.  Shake the bag, and travel from student to student, having each student draw 3 cubes from the bag (without replacement, or all 3 at once, doesn’t matter).  If they are able to draw exactly 2 whites and a red from the bag, they receive a Jolly Rancher reward.

After every student has had a chance to play, I add an additional challenge to the game.  Letting the class know that there are exactly 20 cubes in the bag, can they predict the distribution of colors in the bag, using the information gathered from the pulls they observed as evidence?  Students who can guess the exact distribution also win the coveted Jolly Ranchers.

Next, dump out the cubes to show the true distribution.  Was the 2 white, 1 red game “winnable”?  Was it possible to win?  Was it plausible that one would win?  I usually try to rig the color distribution so that one can win about 25% of the time.  The 10 white, 6 red, 4 blue configuration will provide a 23.6% probability of winning.

STATISTICAL TALES OF THE IMPROBABLE

Always remind your students that probability is a long-term ratio.  The 1/6 probability of rolling a five on a die does not mean that every 6th roll will be a five.  In the short term, strange things can happen.

The CBS show “The Amazing Race” provided a great probability teaching moment in its 6th season.  In a “Pit Stop”, teams must complete a challenge in order to earn a clue and move on in the race.  Here’s a summary of the challenge:

In a field are 270 large hay bales.  20 of the bales contain clues.  You must continue to roll out hay bales until you locate one with a clue, at which time you can move on.

Think about these openers:

• What is the probability you select a bale with a clue on your first attempt?
• What is the probability you select a bale with a clue on your second attempt?  Third attempt?
• What is the probability it takes you 5 or more bales to locate a clue?
• What is the probability you roll out 20 bales, and do not find a clue?

The clip from this show appears below.  You’ll love the reactions of your students!

One last example tale comes from the world of gambling.  While I try to stay away from too much gambling talk in classes, this die-rolling activity leads to a neat backstory.  Have your students roll pairs of dice, and record the number of rolls needed to roll a sum of 7.  After a 7 is rolled, start a new count.  Plotting the results in a class dotplot gives a nice example of a skewed-right distribution, which is often a new shape for our students.

In class, what was the most number of rolls needed?  I have had students get into the 20’s or 30’s.  Is it possible that it could take 50 rolls to get a sum of 7?  Is it plausible?  Note the subtle language lesson happening.

Now, on to craps.  Craps is a fairly complex game, which boils down to this for our example:  once a player rolls, they continue winning until a sum of 7 is rolled, at which point the round ends.

Meet Pat DeMauro:

Pat visited the Borgata casino in Atlantic City in May, 2009 and set the world record for a game of caps, by tossing the dice 154 times without rolling a 7!

Pat’s winning streak was featured in Time Magazine, and features some of the details of the record run.

Probability is exciting!  Make it so!