ELAC Theoretical and Experimental Probabilities Project
Final Project Details:
In your project, you will be performing an experiment, and calculating a number of probabilities.
The real point of the project is to gain a deep understanding of the difference between two different types of probabilities:
Theoretical Probability: “Probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes.”
Experimental Probability: “Probability based on an experiment written as a ratio comparing the number of times the event occurred to the number of trials.”
Here is what you need to do for the project:
(Along with describing the steps you need to perform to complete your Final Project, I have included an example of what you will be submitting to me.)
Step #1) Select a candy that comes in a bag, which has randomly colored pieces. (Ex: M&M’s, Skittles, Star Bursts, Gummy Bears/Worms) Make sure it has at least 50 pieces, or buy a few bags, and combine them. (If you have trouble gaining access to the materials, just let me know, and I will be able to assist you.)
EXAMPLE:
I have decided to use a bag of M&M’s
Step #2) Select a random candy and record it’s color in a table. Put it back in the bag, shake it up and select another. Do this 25 times. You will use this to calculate your experimental probabilities.
EXAMPLE:
|
Color |
Probability |
Probability (Decimal) |
|
Red |
4/25 |
.16 |
|
Yellow |
5/25 |
.20 |
|
Orange |
3/25 |
.12 |
|
Blue |
5/25 |
.20 |
|
Green |
5/25 |
.20 |
|
Brown |
3/25 |
.12 |
Step #3) If there were 1,000 pieces of candy in a bag, how many of each color would you expect to find?
EXAMPLE:
Red: = (.16)(1000) = 160
Blue: = (.20)(1000) = 200
Yellow: = (.12)(1000) = 120
Green: = (.20)(1000) = 200
Orange: = (.20)(1000) = 200
Brown: = (.12)(1000) = 120
Step #4) Count how many pieces of candy are actually in your bag, noting the number of each color; use this to calculate the theoretical probabilities.
EXAMPLE:
My bag contained 57 M&M’s
|
Color |
Total |
Probability |
Probability (Decimal) |
|
Red |
9 |
9/57 |
.1579 |
|
Yellow |
10 |
10/57 |
.1754 |
|
Orange |
8 |
8/57 |
.1404 |
|
Blue |
12 |
12/57 |
.2105 |
|
Green |
11 |
11/57 |
.1930 |
|
Brown |
7 |
7/57 |
.1228 |
Step#5) Compare the theoretical probabilities to the experimental probabilities by:
- Describing any similarities and differences.
- Justify why you think there are differences and/or similarities.
- Which do you think is more accurate, theoretical or experimental probability? Why?
- What could you do to make either of these probabilities more accurate?
- How would you do this experiment differently?
EXAMPLE:
(This is the part where you have to think, of course…)
Submission Requirements:
- All you need to turn in is your parallel to the example provided, with the addition of discussing the five questions at the end. Your answers to those five questions can be as brief as you would like.
- Everything must be submitted in ONE .PDF file, e-mailed to me
- OR if you finish your project EARLY, by 5/3, you may post it on the Discussion board rather than emailing it. By doing this you will earn credit for BOTH of your required discussions!!!
- YOUR FINAL PROJECT IS DUE, AND MUST BE SUBMITTED BY 5/9 at NOON.
- NO LATE PROJECT WILL BE ACCEPTED!!!
- If you finish your project early, and e-mail it to me by 5/3. I will review it to ensure you will earn full credit by its final due date, (5/9).
