Theoretical probability is all about figuring out how likely an event is to happen based on math, not by actually doing the experiment. It's the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, when you flip a fair coin, the theoretical probability of getting heads is $\frac{1}{2}$ because there's one way to get heads and two possible outcomes (heads or tails). Understanding theoretical probability helps us make predictions and understand the world around us! 🎉
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Probability | A. The set of all possible outcomes of an experiment. |
| 2. Outcome | B. A result of an experiment. |
| 3. Event | C. The chance that something will happen. |
| 4. Sample Space | D. A specific set of outcomes. |
| 5. Theoretical Probability | E. Probability based on reasoning, not experiments. |
Answers: 1-C, 2-B, 3-D, 4-A, 5-E
Complete the following paragraph using the words: favorable, total, probability, event, outcome.
The _______ of an _______ is calculated by dividing the number of _______ outcomes by the _______ number of possible outcomes. Each possible result is called an ______.
Answers: probability, event, favorable, total, outcome
Imagine you have a bag with 3 red marbles and 5 blue marbles. If you pick one marble without looking, what is the theoretical probability of picking a red marble? Explain your answer.
Answer: The theoretical probability of picking a red marble is $\frac{3}{8}$. This is because there are 3 red marbles (favorable outcomes) and a total of 8 marbles (total possible outcomes). The probability is calculated as: $P(red) = \frac{number\ of\ red\ marbles}{total\ number\ of\ marbles} = \frac{3}{8}$.
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