Probability+Activity+-+An+Experiment+with+a+Die

=Activity: An Experiment with a Die=
 * You will need:
 * A single [|die] || [[image:http://www.mathsisfun.com/geometry/images/single-die.jpg width="83" height="112"]] ||  ||

Interesting point
Many people think that one of these cubes is called "a dice". But no! The **plural is dice**, but the singular is **die**. (i.e. 1 die, 2 dice.) The common die has six faces: We usually call the faces 1, 2, 3, 4, 5 and 6.

High, Low, and Most Likely
Before we start, let's think about what might happen. The first two questions are quite easy to answer: Are they all just as likely? Or will some happen more often? Let us see which is most likely ...
 * Question: If you roll a die:**
 * 1. What is the **least** possible score?
 * 2. What is the **greatest** possible score?
 * 3. What do you think is the **most likely** score?
 * 1. The **least** possible score must be **1**
 * 2. The **greatest** possible score must be **6**
 * 3. The **most likely** score is ... ???

The Experiment
**Throw** a die 60 times,

**record** the scores in a tally table. You can record the results in this table using [|tally marks]: OK, Go! ... ... Now draw a bar graph to illustrate your results. You can fill in this one: Or you can use [|Data Graphs (Bar, Line and Pie)]
 * Score || Tally || Frequency ||
 * 1 ||  ||   ||
 * 2 ||  ||   ||
 * 3 ||  ||   ||
 * 4 ||  ||   ||
 * 5 ||  ||   ||
 * 6 ||  ||   ||
 * || Total Frequency = || 60 ||
 * **Finished ...?**

then print it out. ||  ||  ||
 * You may get something like this: ||  || [[image:http://www.mathsisfun.com/activity/images/die-results.gif width="220" height="152"]] ||
 * Are the bars all the same height?
 * If not ... why not?

60 Throws
OK, why did I ask you to make **60** throws? Well, only 6 throws would not give you good results, 600 throws would have been too hard, so I chose 60, which is **10 lots of 6**. So we should **expect** **10** of each number, like this:

Those are the **theoretical** values,

as opposed to the **experimental** ones you got from your **experiment**!

How do those theoretical results compare with your experimental results? This graph and your graph should be **similar**, but they are not likely to be exactly the same, as your experiment relied on **chance**, and the number of times you did it was fairly small. If you did the experiment a very large number of times, you would get results much closer to the theoretical ones.

Questions
An experiment gives results. When done again it may give **different** results! So it is important to know when results are **good quality**, or just **random**.
 * Which face came up most often? ____
 * Which face came up least often? ____
 * Do you think you would get the same results if you did this again? Yes / No

Probability
On the page [|Probability] you will find a formula:
 * Probability of an event happening = ||  || Number of ways it can happen ||
 * ^  ||^   || Total number of outcomes ||
 * ^  ||^   || Total number of outcomes ||

Example: Probability of a 2
We know there are 6 possible outcomes. And there is only 1 way to get a 2. So the probability of getting 2 is: Doing that for each score gets us: The sum of all the probabilities is **1** For any experiment: The sum of the probabilities of **all** possible outcomes is always equal to **1**
 * Probability of a 2 = ||  || 1 ||
 * ^  ||^   || 6 ||
 * ^  ||^   || 6 ||
 * Score || Probability ||
 * 1 || 1/6 ||
 * 2 || 1/6 ||
 * 3 || 1/6 ||
 * 4 || 1/6 ||
 * 5 || 1/6 ||
 * 6 || 1/6 ||
 * || Total = 1 ||

=Reference=

@http://www.mathsisfun.com