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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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Q: How would you compare theoretical probability and experimental probability for getting three heads to the theoretical probability. would you expect the probabilities to be equal .?
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Continue Learning about Statistics

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One way to estimate the probability of an event is to use a theoretical model to compare the relative likelihood of the event compared to all possible outcomes.


What is prior classical probability?

When you throw a die, there are six possibilities. The probability of a number from 1 to 6 is 1/6. This is classical probability. Compare this with empirical probability. If you throw a die 100 times and obtain 30 sixes, the probability of obtaining a 6 is 30/100 or 0.3. Empirical probabilities change whereas classical probability doesn't.


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Compare experimental and theoretical probability?

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In theoretical probability, the probability is determined by an assumed model (for example, the normal distribution). (compare with empirical probability)


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If you were to perform the experiment 1000 times how would the experimental probality compare to the theoretical probality?

In order to answer this question it is important, first, to be certain that the theoretical probability (not probality!) can be calculated. For example, there is a probability that the first car that I see being driven on the next day [tomorrow] is black but I challenge anyone to calculate the theoretical probability. No one, not even I, know when I will wake up tomorrow (assuming that I live to wake up), when I draw my curtains and when look into the street. The number of black cars and non-black cars in my locality can be found, but it could be a car from somewhere else which just happens to drive past at the critical moment.Assuming there was a theoretical probability, the experimental probability would be better than would be obtained from 999 trials and not as good as 1001 trials. Any other statements would depend on the distribution of the variable being observed.


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What is prior classical probability?

When you throw a die, there are six possibilities. The probability of a number from 1 to 6 is 1/6. This is classical probability. Compare this with empirical probability. If you throw a die 100 times and obtain 30 sixes, the probability of obtaining a 6 is 30/100 or 0.3. Empirical probabilities change whereas classical probability doesn't.


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