# Probability and Real World Probability

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There are 2 types of probability: empirical and theoretical (classical).

- Define the 2 probability types in your own words.

- List 1 profession example for each probability type: empirical probability and theoretical (classical) probability. Explain clearly how these probabilities are used.

- List a real-world probability problem for your peers to solve. Your peers will have the opportunity to work your problem and receive feedback from you as the discussion progresses. Be sure to go back and respond to those who solved your problem or who need help with solving it.

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The probability and real world probabilities examples are analyzed.

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There are 2 types of probability: empirical and theoretical (classical)

Define the 2 probability types in your own words.

The Theoretical (or Classical) approach to assigning probabilities to specific events makes the fundamental assumption that every one of the possible outcomes is equally likely. So, if there are "n" total possible outcomes that are all equally likely, then the probability of any one of them would be 1/n. As an example, suppose that you have a six-sided die that you believe is a fair six-sided die. What this means in the context of rolling the die is that each of the six possible outcomes is equally likely to be the result when the die is rolled. In this case then, we have what we believe are "n" = 6 equally likely outcomes and so without even rolling the die once we could say (taking the Classical approach to assigning probabilities) that the probability that you obtain a 4 as your result when you roll this six-sided die would be 1/6 = 0.16666 ... = 16.67%.

On the other hand, the Empirical (or Relative Frequency) approach to assigning probabilities makes no assumptions at all about any of the probabilities of any of the outcomes. In an Empirical approach to estimating or calculating probabilities the exact same experiment is simply repeated a large number of times (say "n" times) and the frequency of occurrence (say "f") of the outcome of interest in those "n" identical repetitions of the experiment is counted. In this case, the empirical approach to estimating the probability that the event of interest happens would be "f"/"n". As an example, suppose that you had the same six-sided die as above, and that you once again wanted to estimate the probability that when you rolled the six-sided die one time the result was a 4. You could estimate this probability as we did above with the Classical approach, or you could take ...

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