~ The theoretical probability is the outcome, found by data alone. It is called the theoretical probability because it uses data to find the outcome. You can find it by analyzing the data of the outcome.
Here is an example:
Suppose there are 3 marbles in a box. One red, one yellow, and one blue. The theoretical probability of picking one yellow marble out from the box is 1/3. This is because there are 3 possible outcomes: red, yellow, or blue. Picking one yellow marble is one outcome out of 3. Therefore, the theoretical probability of picking one yellow marble is 1/3.
2.
a) Suppose two people do an experiment to estimate the probability of an outcome. Will they get the same probabilities? Explain.
~ It is highly unlikely for them to get the same probabilities. When conducting an experiment people usually end up with different results.
b) Two people analyze a situation to find the theoretical probability of an outcome. Will they get the same probabilities? Explain.
~ Yes. Since the theoretical probability is based on evidence and reasoning, they should probably get the same probabilities.
c) One person uses an experiment to estimate the probability of an outcome. Another person analyzes the situation to find the theoretical probability of an outcome. Will they get the same probabilities? Explain.
~ They will probably not get the same probabilities because as I said before, theoretical probabilities are more precise since it is based on data; whereas finding the probability from an experiment has proof, but the results are not certain.
3. What does it mean for a game to be fair?
~ For a game to be "fair", means that all of the outcomes are equally likely. One example of this is going back to the marble scenario. If there are the same number of each color marbles, the same size, shape, etc. It is fair. This is because there is an equally likely chance for each marble to be picked.
4. What is a sample space, and how can it be represented?
~ A sample space is a way to represent your data. There are many different ways to show this, such as a tree diagram on the left.
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Elena, your ideas are correct, but be careful with your word choice. The use of the word "data" in the first response is not entirely correct. A better term would be "analyzing outcomes".
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