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Q: What is the difference between theoretical and experimental probability?

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The difference between experimental probability and theoretical probability is that experimental probability is the probability determined in practice. Theoretical probability is the probability that should happen. For example, the theoretical probability of getting any single number on a number cube is one sixth. But maybe you roll it twice and get a four both times. That would be an example of experimental probability.

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probability is a guess and actuality is what will happen

Probability is the likelihood, expressed in numerical or ratiometric terms, that an event will occur. A probability of 1 means that the event will occur. A probability of 0 means that the event will not occur. A probability of 0.5 means that the likelihood of the event occurring is equal to the likelihood of it not occurring. For instance, a fair coin has a 0.5 probability of being heads, and a 0.5 probability of being tails. Defined formally, probability is the number of permutations of the desired outcome divided by the number of permutations of all possible outcomes. Take a standard six-sided die, for instance. There are six permutations. One of them is a 1, so the probability of rolling a 1 is 1 in 6, or about 0.1667. Probability is not assured. If you roll a die 600 times, you will not necessarily get 100 1's. Over the long run, you will approach that outcome, but each trial will have different results. This is the difference between theoretical probability and experimental probability - theoretical being the mathematical estimate - experimental being the observed results.

I'm going to assume you're looking for the probability of getting three heads out of three coin spins and that you're using a fair coin. For coin spins, theoretical probability is very simple. The probability of getting three heads in a row is 1/2 * 1/2 * 1/2 = 1/8. This means that if you tossed a coin three times, you'd expect to see three heads once every 8 trials. For experimental probability you need to define clear trials, for this experiment you can't just spin a coin over and over and count the number of times you see three heads in a row, for example, if you threw the following: H T H H T T H H H H H T T H T T T you have three cases where you have three heads in a row, but they all overlap so these are not independent trials and cannot be compared to the theoretical result. When conducting your experiment, you know that if you get a T in your trial, it doesn't matter what comes after, that trial has already failed to get three heads in a row. The trial is deemed a success if you get three heads in a row, naturally. As a result, if you threw the above sequence, you would to determine your experimental probability in the following way: H T fail H H T fail T fail H H H success H H T fail T fail H T fail T fail T fail In this example we have 8 trials and one success, therefore the experimental probability is 1/8. The sample variance (look it up), however is also 1/8, meaning that all you really know is that the experimental probability could be anywhere between 0 and 1/4. The only way to get the variance down (and therefore reduce your confidence interval) is to perform more and more trials. It's unlikely for the theoretical probability and experimental probability to be EXACTLY the same but the more trials you do, the more the experimental probability will converge on the theoretical probability.

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The difference between experimental probability and theoretical probability is that experimental probability is the probability determined in practice. Theoretical probability is the probability that should happen. For example, the theoretical probability of getting any single number on a number cube is one sixth. But maybe you roll it twice and get a four both times. That would be an example of experimental probability.

experimental probability involves conducting numerous amounts of trials of an experiment and theoretical is determining that a certain outcome will occur through reasoning and calulation.

They are probabilities: that is, estimates of the likelihood of an event happening.

Theoretical value and experimental value

expiremental: finding the answer by observing it lots of times.. theoretical: its like a theory,, you just guess!!~ <3

Empirical anything is what is observed. Theoretical is a calculation of what things ought to be.

empirical probability is when you actually experiment with it and get data values, and theoretical probability is when you use math to make an educated guess.

mostly, how good your theory is. Remember, experimental values are from reality.

They are exactly the same

In experimental probability the probabilities of the outcomes are calculated as the proportion of "successful" outcomes in repeated trials. In theoretical probability these are calculated on the basis of laws of science being applied to a model of the experiment. For example, to find the probability of rolling a six on a standard die, you could roll the die many times (N) and count the number times that it comes up 6 (n). The experimental probability is n/N. The theoretical approach would be to work from the principle that each outcome was equally likely - since it is a fair die - and since the total probability must be 1, the probability of any one face must be 1/6. The second method will only work if there is a good mathematical model.

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