When do we use experimental probability

To see this, the number trials should be sufficiently large in number. Experimental probability is frequently used in research and experiments of social sciences, behavioral sciences, economics and medicine. In cases where the theoretical probability cannot be calculated, we need to rely on experimental probability. For example, to find out how effective a given cure for a pathogen in mice is, we simply take a number of mice with the pathogen and inject our cure.

We then find out how many mice were cured and this would give us the experimental probability that a mouse is cured to be the ratio of number of mice cured to the total number of mice tested. In this case, it is not possible to calculate the theoretical probability.

We can then extend this experimental probability to all mice. It should be noted that in order for experimental probability to be meaningful in research, the sample size must be sufficiently large.

In our above example, if we test our cure on 3 mice and all of these are cured, then the experimental probability that a mouse is cured is 1. Siddharth Kalla Jul 16, Usually the probabilities depend on many different factors and it is not possible to account for them all to figure out the probability exactly, here we use experiments to learn the probabilities from the data.

As for "known", or "theoretical" probabilities, they occur either in probability textbooks, or are just guesses to be used as a priors, or for making back-of-the-envelope guesstimates, but rather nowhere else. Before to give a proper answer to your question we have to give an answer to another one: what are probabilities? Reply to this question is far from trivial.

Any reply to your question should be preceded from a disentanglement about the definition. The idea behind this approach starting from "ignorance" about the quantification of probabilities of some events. Frequentist approach refuse the priori of equiprobability assumption. Following a frequentist approach: after the experiment, under replicability condition and when the proper convergence are at acceptable level, we achieve a good estimate of the two probabilities.

In theoretical examples we can always consider probabilities are given. No experiments, only calculus follow. In practical cases, priori about probabilities, in terms of equiprobability or others assumption, remain always debatable. Unfortunately even the reliability of conditions like: replicability and proper convergence are always debatable.

In case like gambling the equiprobability hypothesis is widely accepted, in most case tacitly. Sometimes experiment are conducted in critique or confirmation fashion. In many others case frequentist approach are follow. Ultimately, what to do in any practical case is a your choice. Debate about the meaning of probability have a long and interesting history. Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial.

The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. For instance, you flip a coin 30 times and record whether you get a head or a tail. The experimental probability of obtaining a head is calculated as a fraction of the number of recorded heads and the total number of tosses. The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted.

Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. Consider an experiment of rotating a spinner 50 times. The table given below shows the results of the experiment conducted. Let us find the experimental probability of spinning the color - blue. Experimental results are unpredictable and may not necessarily match the theoretical results. We can simply continue the experimental by flipping the coin for many more times —say, 20, times.

When more trials are performed, the difference between experimental probability and theoretical probability will diminish. The experimental probability will gradually get closer to the value of the theoretical probability.

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