Theoretical Probability

Grade 7 Math Worksheets

Theoretical probability, also known as classical probability or a priori probability, refers to the mathematical calculation of the likelihood or chance of an event occurring based on theoretical principles and assumptions.

Table of Contents:

What is Theoretical Probability
Examples
FAQs

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Theoretical Probability - Grade 7 Math Worksheet PDF

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What is Theoretical Probability?

It is a measure of probability that is determined by analyzing the underlying structure and properties of an experiment or event.

Theoretical Probability Formula

P(event) = Number of favorable outcomes / Total number of possible outcomes

This formula represents the ratio of the number of favorable outcomes to the total number of possible outcomes. By dividing the number of favorable outcomes by the total number of outcomes, we can determine the probability of the event occurring.

Theoretical Probability Formula

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Example

Suppose we have a bag with 10 red balls and 5 blue balls. To find the theoretical probability of drawing a red ball, we use the formula: P(red) = Number of favorable outcomes / Total number of possible outcomes. In this case, the number of favorable outcomes is 10 (as there are 10 red balls), and the total number of possible outcomes is 15 (since there are a total of 15 balls in the bag). Thus, the theoretical probability of drawing a red ball is 10/15, which simplifies to 2/3 or approximately 0.667. Therefore, the theoretical probability of drawing a red ball is 2/3 or approximately 0.667.

How to find Theoretical Probability

Define the sample space: Identify all possible outcomes of the experiment or event.

Example: Consider flipping a fair coin. The sample space consists of two possible outcomes: heads (H) or tails (T).

Determine the favorable outcomes: Identify the outcomes that meet the desired condition or criteria for the event.

Example: Suppose we want to find the probability of getting heads (H). In this case, the favorable outcome is heads.

Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes.

Example: Number of favorable outcomes = 1 (since there is one way to get heads) Total number of possible outcomes = 2 (since there are two possible outcomes, heads or tails)

Therefore, the theoretical probability of getting heads when flipping a fair coin is: P(heads) = Number of favorable outcomes / Total number of possible outcomes = 1/2 = 0.5 or 50%

So, the theoretical probability of getting heads when flipping a fair coin is 0.5 or 50%.

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Theoretical Probability FAQS

What is theoretical probability?

Theoretical probability, also known as classical probability, is the calculation of the likelihood of an event based on theoretical principles and assumptions. It is determined by analyzing the underlying structure and properties of an experiment.

How is theoretical probability calculated?

Theoretical probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The formula is: P(event) = Number of favorable outcomes / Total number of possible outcomes.

What does the theoretical probability represent?

Theoretical probability represents the idealized probability of an event occurring based on mathematical calculations and assumptions. It provides a model for predicting the likelihood of different outcomes in an ideal scenario.

What is the sample space in theoretical probability?

The sample space is the set of all possible outcomes of an experiment or event. It is used to define the scope of the possible outcomes that are considered when calculating theoretical probability.

What does a probability of 0 mean in theoretical probability?

A probability of 0 means that the event is impossible and cannot occur in the given scenario. It indicates that there are no favorable outcomes among the possible outcomes.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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