A fair coin has 2 sides (heads and tails) that are equally likely to show when the coin is flipped. A person claims that if you flip a fair coin, the probability of getting a head is 50% because the coins is fair and both sides are equally likely to land face up. Is this an example of a theoretical probability or an empirical probability

Theoretical probability is the theory behind probability.To find the probability of an event using theoretical probability,it is not required to conduct an experiment.

The theoretical probability is defined as the ratio of the number of favorable outcomes to the number f possible outcomes.

probability of event(P(E)=[tex]\frac{no.of favorable outcomes}{no.of possible outcomes}[/tex]

Empirical probability:-

The definition of probability breaks down when do not have a complete priori analysis , that is when the outcomes of the trial are not equally likely or when the total number of trials is infinite or when the enumeration of all equally likely events is not possible.so this is called statistical or empirical definition of probability or experimental probability.

Probability of event P(E) =[tex]\frac{no.of times that event occurs}{total number of trials}[/tex]

The basic difference between these two approaches is that in the experimental approach,the probability of an event is based on what has actually happened by conducting a series of actual experiments and the theoretical approach we attempt predict what will occur without actually performing the experiments.

Given example is equally likely events so this is theoretical probability.