Concept of Objective Probability
Probabilities with different probable outcomes
Interpret the limit of relative frequencies of an event as its probability
Probabilities and relative frequency
- Idea: Define probabilities as limits of relative frequencies
- Informal: Conduct the experiment \(n\) times independently and check how often the desired outcome \(\omega\) was thrown. Then divide it by \(n\) and you obtain the relative frequency for \(\omega\). Note: the larger \(n\), the more precise the relative frequency (and therefore the probability)
Above you can see how the relative frequencies converge over larger repetitions to \(0.5\)
The objectivist concept of probability
In practice we can now approximate the probabilities of events well if we perform enough repetitions.
Calculation rules for Laplace probablilties are also valid for the now following objective probabilities
Now: The probability of each event \(A\) can be calculated from the probabilities of the contained outcomes \(\omega\)
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