objective relative frequency interpretation

This relative frequency interpretation of probability is said to be objective because it rests on a property of the experiment rather than on any particular individual concerned with the experiment. For example, two different observers of a sequence of coin tosses should both use the same probability assignments since the observers have nothing to do with limiting relative frequency. In practice, this interpretation is not as objective as it might seem, since the limiting relative frequency of an event will not be known. Thus we will have to assign probabilities based on our beliefs about the limiting relative frequency of events under study.

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Fortunately, there are many experiments for which there will be a consensus with respect to probability assignments.

• When we speak of a fair coin, we shall mean $P\left(H\right)=P\left(T\right)=.5$
• a fair die is one for which limiting relative frequencies of the six outcomes are all $1/6$ , suggesting probability assignments $P\left(\{1\}\right)=\cdots =P\left(\{6\}\right)=1/6$.

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