### Understanding Probability

This lesson is designed to help students understand the mechanics of experimental probability. Second, it is also a good way for students to make a link between the difference in experimental probability and theoretical probability. And finally, it helps students to organize data in a neat and orderly manner.

1. Introduce a cloth bag (or a hat) and tell the students that there are 12 blocks inside. This is the only information you will give the students. Before the lesson, choose 12 blocks (chips, pens, etc) and put them in the bag. I use 4 different colors in my bag in the following denominations, 6, 3, 2, 1; because these numbers are easily divisible by 12, 6, 4, 3, 2) to find a probability percentage. Of course, all the students know is that you have 12 blocks in the bag, they know nothing about the number of colors not the quantities of each color.

2. Explain to the the students that you are going to pull out one block at a time, they record will record it, and you will put it back in the bag.  The objective of the activity, determine how many of of each color block is in the bag using experiential probability.  There are several key points you will be looking for, or will need to help your learners with:

• Let them come up with their own system for recording the data.  Most will choose a tally or a table.  After you have pulled about ten blocks, it would be useful to stop and ask the students to share their recording methods in a Think/Pair/Share.  Give time for students to readjust their method.

• Let the students determine how many trials you will do.  Ask them before you start how many pulls they think they need to figure out the problem.  Once you get to that number, you can reevaluate if it was enough.

The math on this may give them a problem.  Once, you have done enough trials, ask the students to try and solve the puzzle.  The key to figuring out the puzzle is by finding the fraction or percent of the trails, and then applying that to the bag.  For example, if there were 20/80 blocks in the trial that were red, that means that 1/4 (or 25%) of the trial pulls were red.  The conclusion that one could make from this is that there are 25% red blocks in the bag, and 25% of 12 is 3.