Experimental Probability

Probability can also be measured by doing the experiment or process repeatedly. The experimental probability or relative frequency probability of an event A is given by the formula

For example, using the formula for the theoretical probability, the probability of obtaining a head if you toss a coin is $\frac{1}{2}=\mathrm{0.5.}$

In an actual experiment, obtaining 7 heads after tossing the coin 10 times, for instance, will give a relative frequency probability for obtaining a head, $P(A)=\frac{7}{10}=\mathrm{0.7.}$ Of course, the relative frequency probability would change from trial to trial.

However, if the experiment is done several number of times (may be a large number of times), as N becomes larger, the experimental probability will tend to converge to the value of the theoretical probability of the event.

Remember that the greater the number of trials in an experiment, the closer the value of the experimental probability with that of the theoretical probability.