experimental probability vs theoretical probability quiz

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Probability: Theoretical vs. Experimental Probability Concepts

Study Flashcards

10 Questions

What does the sample space represent.

The set of all possible outcomes from an experiment

How are events defined in probability theory?

By a certain condition that applies to only one outcome

What do outcomes refer to in probability?

Individual results produced during an experiment

Why is defining the sample space crucial in probability?

To help identify different events and their respective probabilities

In probability theory, what could events include?

Getting an even number while rolling a die

What is theoretical probability?

The calculation of probabilities using mathematical formulas

Which type of probability involves testing a hypothesis or scenario?

Experimental probability, what does sample space represent in probability.

The set of all possible outcomes in an experiment

In theoretical probability, what does the calculation rely on?

Assumptions or predefined characteristics

How is experimental probability determined?

Through observation or trials

Study Notes

Probability.

Probability is a branch of mathematics that deals with random events and their likelihood of occurrence. There are two main types of probability: theoretical probability and experimental probability. Understanding these concepts is essential for understanding how to measure and analyze chance events. In this article, we will explore the concepts of theoretical probability, experimental probability, sample space, events, and outcomes.

Theoretical Probability

Theoretical probability refers to the calculation of probabilities using mathematical formulas. It involves determining the likelihood of an event occurring based on given information about the situation. For example, if you have a deck of cards with 52 cards and want to find out what percentage of them are hearts, you would calculate the theoretical probability by dividing the number of hearts by the total number of cards. This type of probability does not involve actual experiments; rather, it relies on assumptions or predefined characteristics of sets of events.

Experimental probability is determined through observation or trials. It involves the actual testing of a hypothesis or scenario to determine the likelihood of an outcome occurring. For instance, if you flip a coin ten times and record the results, the proportion of heads and tails observed represents the experimental probability of getting either answer when flipping the coin once. This method provides real-world data that can be used to compare against theoretical probabilities and understand any discrepancies between the two.

Sample Space

Sample space refers to the set of all possible outcomes from an experiment. These outcomes represent every value that could result from performing the trial. To illustrate, consider tossing a fair six-sided die. The sample space consists of the numbers 1 through 6, representing each potential outcome when rolling the die. Defining the sample space is crucial because it helps us identify different events and their respective probabilities.

Events within probability theory refer to specific outcomes or combinations of outcomes. They are defined by a certain condition, which may apply to one or more outcomes within the sample space. For example, in the case of the die roll, events could include getting an even number, odd number, or a number less than four. Event definitions help us categorize and analyze the results of experiments, allowing us to make informed decisions about the likelihood of various scenarios.

Outcomes refer to individual results produced during an experiment. Each possible outcome belongs to exactly one event and contributes to the overall sample space. Using our die roll example again, the outcome could be the specific number rolled, such as 3 or 4, which falls under the event category of getting an odd number. By analyzing the distribution of outcomes across events, we can gain insights into the relative frequency of each possible outcome within the sample space.

In conclusion, probability is a vital concept in mathematics and science, helping us make sense of uncertain situations. Through understanding theoretical probability, experimental probability, sample space, events, and outcomes, we can better predict and analyze the likelihood of various events, leading to more informed decision-making.

Explore the fundamental concepts of theoretical probability, experimental probability, sample space, events, and outcomes in the realm of probability theory. Learn how to calculate probabilities using mathematical formulas and how to determine likelihood through observation or trials. Enhance your understanding of random events and their probabilities.

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AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 7.

• Intro to theoretical probability
• Experimental versus theoretical probability simulation

Theoretical and experimental probability: Coin flips and die rolls

• Random number list to run experiment
• Random numbers for experimental probability
• Interpret results of simulations

Part 1: Flipping a coin

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
• (Choice A)   Results from an experiment don't always match the theoretical results, but they should be close after a large number of trials. A Results from an experiment don't always match the theoretical results, but they should be close after a large number of trials.
• (Choice B)   Dave's coin is obviously unfair. B Dave's coin is obviously unfair.
• (Choice A)   The experimental probability got closer to the theoretical probability after more flips. A The experimental probability got closer to the theoretical probability after more flips.
• (Choice B)   The experimental probability got farther away from the theoretical probability after more flips. B The experimental probability got farther away from the theoretical probability after more flips.

Part 2: Rolling a die

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Theoretical vs. Experimental Probability: How do they differ?

Probability is the study of chances and is an important topic in mathematics. There are two types of probability: theoretical and experimental.

So, how to define theoretical and experimental probability? Theoretical probability is calculated using mathematical formulas, while experimental probability is based on results from experiments or surveys. In order words, theoretical probability represents how likely an event is to happen. On the other hand, experimental probability illustrates how frequently an event occurs in an experiment.

Read on to find out the differences between theoretical and experimental probability. If you wonder How to Understand Statistics Easily , I wrote a whole article where I share 9 helpful tips to help you Ace statistics.

Table of Contents

What Is Theoretical Probability?

Theoretical probability is calculated using mathematical formulas. In other words, a theoretical probability is a probability that is determined based on reasoning. It does not require any experiments to be conducted. Theoretical probability can be used to calculate the likelihood of an event occurring before it happens.

Keep in mind that theoretical probability doesn’t involve any experiments or surveys; instead, it relies on known information to calculate the chances of something happening.

For example, if you wanted to calculate the probability of flipping a coin and getting tails, you would use the formula for theoretical probability. You know that there are two possible outcomes—heads or tails—and that each outcome is equally likely, so you would calculate the probability as follows: 1/2, or 50%.

How Do You Calculate Theoretical Probability?

• First, start by counting the number of possible outcomes of the event.
• Second, count the number of desirable (favorable) outcomes of the event.
• Third, divide the number of desirable (favorable) outcomes by the number of possible outcomes.
• Finally, express this probability as a decimal or percentage.

The theoretical probability formula is defined as follows: Theoretical Probability = Number of favorable (desirable) outcomes divided by the Number of possible outcomes.

How Is Theoretical Probability Used in Real Life?

Probability plays a vital role in the day to day life. Here is how theoretical probability is used in real life: 

• Sports and gaming strategies
• Analyzing political strategies.
• Buying or selling insurance
• Determining blood groups 
• Online shopping
• Weather forecast
• Online games

What Is Experimental Probability?

Experimental probability, on the other hand, is based on results from experiments or surveys. It is the ratio of the number of successful trials divided by the total number of trials conducted. Experimental probability can be used to calculate the likelihood of an event occurring after it happens.

For example, if you flipped a coin 20 times and got heads eight times, the experimental probability of obtaining heads would be 8/20, which is the same as 2/5, 0.4, or 40%.

How Do You Calculate Experimental Probability?

The formula for the experimental probability is as follows:  Probability of an Event P(E) = Number of times an event happens divided by the Total Number of trials .

If you are interested in learning how to calculate experimental probability, I encourage you to watch the video below.

How Is Experimental Probability Used in Real Life?

Knowing experimental probability in real life provides powerful insights into probability’s nature. Here are a few examples of how experimental probability is used in real life:

• Rolling dice
• Selecting playing cards from a deck
• Drawing marbles from a hat
• Tossing coins

The main difference between theoretical and experimental probability is that theoretical probability expresses how likely an event is to occur, while experimental probability characterizes how frequently an event occurs in an experiment.

In general, the theoretical probability is more reliable than experimental because it doesn’t rely on a limited sample size; however, experimental probability can still give you a good idea of the chances of something happening.

The reason is that the theoretical probability of an event will invariably be the same, whereas the experimental probability is typically affected by chance; therefore, it can be different for different experiments.

Also, generally, the more trials you carry out, the more times you flip a coin, and the closer the experimental probability is likely to be to its theoretical probability.

Also, note that theoretical probability is calculated using mathematical formulas, while experimental probability is found by conducting experiments.

What to read next:

• Types of Statistics in Mathematics And Their Applications .
• Is Statistics Harder Than Algebra? (Let’s find out!)
• Should You Take Statistics or Calculus in High School?
• Is Statistics Hard in High School? (Yes, here’s why!)

Wrapping Up

Theoretical and experimental probabilities are two ways of calculating the likelihood of an event occurring. Theoretical probability uses mathematical formulas, while experimental probability uses data from experiments. Both types of probability are useful in different situations.

I believe that both theoretical and experimental probabilities are important in mathematics. Theoretical probability uses mathematical formulas to calculate chances, while experimental probability relies on results from experiments or surveys.

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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Experimental vs. Theoretical Probability

6th - 8th grade, mathematics.

11 questions

Introducing new   Paper mode

No student devices needed.   Know more

• 1. Multiple Choice Edit 2 minutes 1 pt Experimental Probability is: What Will happen  What actually happens What should happen What I think Happens
• 2. Multiple Choice Edit 30 seconds 1 pt Experimental probability is: number of times the event occurs/total number of trials  True False
• 6. Multiple Choice Edit 3 minutes 1 pt What is the probability of flipping a coin and getting tails? 1/2 1/3 1/4 Never, Tails never fails.
• 7. Multiple Choice Edit 1 minute 1 pt An experiment consists of rolling a fair number cube. Find the theoretical probability of rolling a 3. 1/6 3/6 1 1/2

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