Q: In which cases would you expect the experimental probability to be closest to the theoretical probability?

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That means that you should roll a die many times, count how often you get the number "2", then divide this by the total number of rolls. If the die is "fair" (no extra weight on one side), you would expect this experimental probability to be somewhere close to the theoretical probability of 1/6, at least, if you roll often enough.

To get the EXPERIMENTAL probability, you'll have to actually carry out the experiment. The EXPECTED probability is equal to a fraction; the numerator will be the number of pieces of papers that have the number 35, the denominator will be the total number of pieces. If you repeat the experiment often, you can expect the experimental probability to be close to the expected probability.

The probability of drawing the Ace of Spades from a standard deck of 52 cards is 1 in 52, or about 0.01923. However, the number of times you can expect to draw it depends on random statistics. If you tested this a large number of times, shuffling the deck each time, you would expect about 1 out of every 52 trials to be the Ace of Spades, but that would only be in the long run, say for thousands and thousands of trials, and even then, it would not be exact. This is the difference between theoretical probability and experimental probability. Theoretical probability is based on pure statistics and the arrangement of the test. All you can say is that, for an infinite number of trials, you would expect 1 out of 52. In the case of experimental probability, you are limited by the number of trials that you can perform. Lets say you ran 10,000 trials. Theoretically, you would expect to draw the Ace of Spades about 192 times. In practice, you would have a range of results.

If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.If a number cube (die) contains the numbers 1, 2, 3, 4, 5, and 6, and the cube is fair, then the probability of rolling a 6 is 1 in 6. If you roll the cube 10 times, you would expect to get 6's 10 / 6, or about 2 times. However, 10 trials is not a lot of trials, so the experimental outcome might not match the theoretical probability. In this case, the experimental probability matched the theoretical probability, but that is simply chance. If you repeat the experiment, so you will probably not get the same results.

The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.

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If you roll a die 100 times, you would expect to get a 1 about 17 times, because the probability of getting a 1 is 1 in 6, or 0.1667. However, that is theoretical probability; experimental probability - the actual results of doing this 100 times - might not be 17, but if you did this a large number of times, the experimental results would indeed begin to approach the theoretical results.

That means that you should roll a die many times, count how often you get the number "2", then divide this by the total number of rolls. If the die is "fair" (no extra weight on one side), you would expect this experimental probability to be somewhere close to the theoretical probability of 1/6, at least, if you roll often enough.

To get the EXPERIMENTAL probability, you'll have to actually carry out the experiment. The EXPECTED probability is equal to a fraction; the numerator will be the number of pieces of papers that have the number 35, the denominator will be the total number of pieces. If you repeat the experiment often, you can expect the experimental probability to be close to the expected probability.

The probability of drawing the Ace of Spades from a standard deck of 52 cards is 1 in 52, or about 0.01923. However, the number of times you can expect to draw it depends on random statistics. If you tested this a large number of times, shuffling the deck each time, you would expect about 1 out of every 52 trials to be the Ace of Spades, but that would only be in the long run, say for thousands and thousands of trials, and even then, it would not be exact. This is the difference between theoretical probability and experimental probability. Theoretical probability is based on pure statistics and the arrangement of the test. All you can say is that, for an infinite number of trials, you would expect 1 out of 52. In the case of experimental probability, you are limited by the number of trials that you can perform. Lets say you ran 10,000 trials. Theoretically, you would expect to draw the Ace of Spades about 192 times. In practice, you would have a range of results.

If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.If a number cube (die) contains the numbers 1, 2, 3, 4, 5, and 6, and the cube is fair, then the probability of rolling a 6 is 1 in 6. If you roll the cube 10 times, you would expect to get 6's 10 / 6, or about 2 times. However, 10 trials is not a lot of trials, so the experimental outcome might not match the theoretical probability. In this case, the experimental probability matched the theoretical probability, but that is simply chance. If you repeat the experiment, so you will probably not get the same 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.

The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.The answer will depend on how soon YOU expect it to arrive! If you think that it will take 5 minutes after you complete the transaction, the probability that it arrives earlier is 0 whereas if you expect it to take 5 moths, the probability that it arrives earlier is 1.

If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.If a number cube (die) contains the numbers 1, 2, 3, 4, 5, and 6, and the cube is fair, then the probability of rolling a 2 is 1 in 6. If you roll the cube 100 times, you would expect to get 2's 100 / 6, or 17 times. However, 100 trials is not a lot of trials, so the experimental outcome might not match the theoretical probability.

Experimental yield is the amount of product obtained from a chemical reaction conducted in a laboratory setting. It is compared to the theoretical yield, which is the amount of product that is predicted to be produced based on stoichiometry calculations. Experimental yield is often less than theoretical yield due to factors such as incomplete reactions, side reactions, or losses during purification.

43/53 = 0.81 : This is not even close to the theoretical probability of 0.50 ; With 0.50, the expected outcome is 26.5 out of 53. I would expect not to get 26 or 27, though - but a range from 21 to 33 (out of 53) would be in my expectations. Imagine coin tosses (probability = 0.5): it is possible to get 43 out of 53, but the chance of this happening is very very small. I don't remember the exact formulas, but consider this: flip a coin 5 times. There are 32 possible outcomes. Only 6 of these 32 would give a 1 out of 5 (or less). This is 6/32 or about 19%. So to get 40 (or more) out of 50, you would need to get 4 (or more) out of 5, ten times, or (6/32)^10 = about 1 in 18 million. To get 43 (or more) out of 53 would be even a smaller chance than this. This is on the scale of chances of winning the lotto (definitely possible, but not probable).

I expect you mean the probability mass function (pmf). Please see the right sidebar in the linked page.

Some but not all scientific models are based on the ability to determine the likelihood that a given experimental outcome has happened by chance alone. If you have an accurate understanding of how the variables in the experiment change when nothing in particular is affecting them, then you have a way to establish some confidence that your outcome is the result of your experimental procedure and not the result of purely random events. The experimental 'lingo' is that the researcher has to determine if the 'Null Hypothesis' can be rejected. The Null Hypothesis is that the experimental outcome is not significantly different from what you would expect if the experiment had no effect at all.As an example, if the probability in the natural world is that some event will happen by chance only one tenth of one percent of the time, then when I observe that event as my experimental outcome, I can be reasonably sure that my procedure has brought about the event; it is so unlikely that it happened by chance. It is not perfect, but few scientific procedures are. This also highlights the importance of replicating studies or of doing meta-analyses of experimental data gathered in many experiments to further reduce the likelihood that observed outcomes are nothing more than chance events.