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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
Which statements are true? Check all that apply.
Answer: ✔ As the number of trials increases, experimental probability is closer to theoretical probability. ✔ As the number of trials increases, there is no change in the theoretical probabilities.
Emma conducted an experiment in which she rolled a six-sided, fair number cube 300 times. How many times would you predict she rolled a 6?
Answer: ✔ Emma conducted an experiment and she rolled a six sided number cube 300 times. The theoretical will be rolling a 6 and it can also be 1/6. 6 would be rolled about (1/6)(300), or it could be 50, times.
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
Answer: ✔ If John rolled a six- sided number and he predicts that it would be 20 times, and my predict would be 3 cause i divided 60 and 20 which gave me 3. And John prediction was to low and the theoretical probability of 1/2, and (1/2)(60) is 30. and also a number cube has 3 even number.
During Samuel's experiment, the experimental probability was 0.25. What else must be true about the experiment?
Answer: ✔ The experimental probability of the outcome is 1/4
Mali performed an experiment with a standard deck of 52 cards. She wanted to see if the face cards (Ace, King, Queen, and Jack) came up the expected number of times when she randomly selected 13 cards from the deck. Mali noticed that the observed frequencies did not match the predicted frequencies. What does she need to change in her experiment to get closer to the predicted values based on the theoretical probability for all the face cards?
Answer: ✔ increase the number of trails
Jamal performed an experiment flipping a coin. He did 10 trials and then his arm got tired. He recorded his results in the table. Based on the experimental probability, Jamal predicted that the number of times the coin lands heads up will always be greater than the number of times it lands tails up. What is the error in his prediction?
Answer: ✔ He did not perform enough trials to compare the theoretical and experimental probabilities.
A six-sided, fair number cube is rolled 100 times as part of an experiment. The frequency of the roll of f the number 3 is 20. Which statement about rolling a 3 is correct?
Answer: ✔ The theoretical probability is 1/6. The experimental probability is 1/5.
A number cube is rolled 60 times. The results of those 60 trials are recorded in the table. Complete the table
Answer: ✔ 1/5 ✔ 2/15
Maya wants to perform an experiment with a spinner labeled A, B, and C. The theoretical probabilities for each section are: P(A) = ½, P(B) = ¼, and P(C) = ¼. Which spinner could she use?
Answer: ✔ the second one, AAAA,BB,CC
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Answer: The theoretical probability is 1/6. The experimental probability is 1/5. Jamal performed an experiment flipping a coin. He did 10 trials and then his arm got tired. He recorded his results in the table. Based on the experimental probability, Jamal predicted that the number of times the coin lands heads up will always be greater than the ...
The experimental probability is 1/15 less than the theoretical probability. Study with Quizlet and memorize flashcards containing terms like Jamal performed an experiment flipping a coin. He did 10 trials and then his arm got tired. He recorded his results in the table. Based on the experimental probability, Jamal predicted that the number of ...
1/2. If a standard number cube (dice) is rolled 4 times and 3 times an even number comes up then what is the theoretical probability of getting an even number? 3/9 or 1/3. A bag has 3 red, 2 green and 4 black ball. If a ball is randomly taken from the bag, find the theoretical probability that it is red. 4/9.
Part 1: Flipping a coin. question a. A fair coin has 2 sides (heads and tails) that are equally likely to show when the coin is flipped. What is the theoretical probability that a fair coin lands on heads? P (heads) =. Check. Explain. question b. Dave flipped a coin 20 times and got heads on 8 of the flips.
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 ...
Answer: Emma conducted an experiment and she rolled a six sided number cube 300 times. The theoretical will be rolling a 6 and it can also be 1/6. 6 would be rolled about (1/6)(300), or it could be 50, times.
Explore the fundamental rules and concepts of probability, including theoretical probability (based on assumptions and calculations) and experimental probability (derived from actual experiments). Learn about random variables (discrete and continuous) and probability distributions (like Bernoulli, binomial, Poisson, and normal distributions). Discover how probability principles are applied in ...
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