What are the odds?

Odds was something that I really struggled with last Spring.  I got it long enough to pass the test, but never really understood it.  I really liked the way this teacher explained it.  She had already taught us how to find the probability of an event happening and I got that pretty good.  So then she explained that the odds in favor are the number of successes over failures.  For some reason, this made a lot more sense this way.

As I searched the internet trying to find something interesting or informative about odds I got very frustrated.  Most of the hits for odds were really for probability.  There were even some that had odds in the title of their worksheets, however they explained probability.  Here is a good page that explains the difference between probability and odds.  It even links to a printable PDF worksheet.

Changing Probability to Odds

I also found a YouTube that illustrates the difference between probability and odds.  Although I must warn you, it is a very silly video - but it makes its point.

A Toast to Probability and Odds

Roll the dice!

We experimented rolling two dice.  We were to roll the pair of dice 36 times.  We had a tally sheet to record the sum of each roll.  Before we began rolling she asked us to predict what sum we thought we would get the most.  I chose 6 just guessing it would be a number that would be in the middle of my choices.

To make things easier (and to reduce the noise level) instead of actually rolling dice she had us use the probability simulator on the calculator.  If you don't have a calculator or dice here is a website that will roll dice for you:

Dice Roll

After 36 rolls, these were my results:

Then she gave us a worksheet to figure out the probability of rolling each sum.  Here is a chart that I found that really shows how much more likely you are to roll a 7 than a 2.

Here's a great website with a worksheet and explanations for a similar activity.

Probability Dice Game

A Simple Flip of a Coin

If you flip a coin what is the probability that you will get heads?  That sounds like an easy enough question - 50% right?  Well theoretically that would be correct. However, we did some experimental probability and ended up with slightly different results.  

Each student was asked to flip a coin 50 times.  Fortunately she showed us how to do that on our calculators so that we didn't actually have to flip a coin.  In my trial I got 23 heads and 27 tails, so not quite 50%, but close.  We added up everyone's coin tosses and again didn't quite make 50%.  Out of 700 coin tosses 327 were heads and 373 were tails.  So 46.7% of the time we ended up with heads.

Here is a great YouTube video to watch if you do not know how to use the coin toss feature on your TI 84 calculator.

TI 84 Probability Simulator

Cereal Toys

When you were a kid, did you ever talk your mom into buying you a box of cereal just so you could have the toy?  I was the youngest of six, so I thought that was why I could never get the toy but we did simulations in probability that helped explain why it is sometimes difficult to collect all the toys that are available.

We were given the task of collecting six different toys from a cereal manufacturer who puts one toy in each box.  First we predicted how many boxes we would need to purchase before we would have all six.  I was not very optimistic - I guessed thirty-six boxes.  Next she had us use the random number generator on our calculator to randomly select numbers from 1 to 6.  She also explained that this could easily be done with a dice or a spinner.  We used a table to tally our results.

I was surprised that it only took me nine boxes of cereal to get all six toys.  However it some other students almost thirty boxes to collect all six.

Here is a great website if you are wanting to teach (or try) this lesson.  It has the cereal lesson plus a couple of more.

Sampling Lessons

Rock, Paper, Scissors

I am paying college tuition to play rock, paper, scissors in class.  Are you serious?  Yes, we really did play rock, paper, scissors in college, but it was a very good way to understand the difference between theoretical probability and experimental probability.

We played the game 45 times recording what each person chose on each play.  We then computed the results and had to determine if we felt it was a fair game.  She explained that since we had just conducted an experiment that was experimental probability.  Next she had us compute the theoretical probability first by completing a matrix and then again using a tree diagram.

Here is a good worksheet that I found if you want to try this out for yourself.
Rock, Paper, Scissors Worksheet

And if you don't have a partner to play with, here is a website that will play against you.
Rock, Paper, Scissors - You vs. the Computer

Tree Diagrams - Pom Poms Help!

We learned about determining probability in multistage experiments. She had us use tree diagrams to help.  The most helpful thing though was she gave us pom poms to use so we could actually do the experiment instead of just dealing with numbers on a paper.

The question was:

"A box contains three white balls and two colored balls.  A ball is drawn at random from the box and not replaced.  Then a second ball is drawn from the box.  Find the probability that the two balls are different colors."

The diagram was so much easier to draw and understand when we could actually do what the question was asking.

Here is a page on Math Is Fun that explains tree diagrams and probability:

Math Is Fun - Probability Tree Diagram

One of the things that I really like about my teacher is that she is not only teaching us the math, but is giving us hands-on activities and advice that we will be able to use with our own students.  She explained that pom poms are great - they are cheap and easy to store.  She also said they work great for working out problems on the board.  You can glue a magnet on the back and they stick to the board.  She suggested that we do not need to go out and buy magnets, but instead when you get a magnet in the mail from a business that you didn't really want and are not interested in, instead of throwing it away cut it up and glue it onto your pom poms.

What is the probability that probability can be fun?

My name is Lisa.  I am attending college working on a degree in elementary / special education.  Currently I am taking a class that is teaching me how to teach math.  I am starting this blog to share the ideas I am learning about teaching probability.  I did not enjoy the section on probability in my college math class, so I have my doubts about how this can be a fun subject to teach.  However my teacher’s enthusiasm is highly contagious so I have hope.

She introduced us to probability by showing us the Monty Hall Problem.  Here is a great YouTube video explaining it.

Monty Hall Problem

It also gave a link to a website where you can try it for yourself.

Stay or Switch? 

I’m still too confused to know if this is going to be fun, but we will see.