Question

Define Empirical probability.

Answer 1

Hint: Empirical probability of any event is calculated by dividing frequency of happening an event to numbers of total trials or outcomes. Therefore, its value always lies between zero and one.

Complete step-by-step answer:
Empirical probability of an event is the probability, which is based on the result of the actual experiment. Hence, it is also known as experimental probability.
Therefore it is defined as the ratio of the number of outcomes in which an event occurred to the total number of trails.
And, it is given as${\displaystyle \frac{f}{n}}$, where f is the frequency of occurrence and n is number of total number of trials.
Empirical probability is different from probability. Empirical probability is completely an experimental based event, while probability is a theoretically based event. We can understand it with the following example.
Let's consider an experiment of throwing a die. In a throw of a die we will get six outcomes (1, 2, 3, 4, 5, and 6). Therefore getting an even number in a single throw of die is (2, 4, and 6). Hence, Empirical probability of getting an even number in a single throw of die is ${\displaystyle \frac{3}{6}}$ or${\displaystyle \frac{1}{2}}=\left(0.5\right)$. Now if we repeat the same experiment instead of throwing one die but throwing one die 10 times. In that case the number of occurrences of even numbers is either less or more than odd numbers. Then in that case probability of getting an even number will be either greater than or less than $0.5$not exactly$0.5$.

Hence, in Empirical probability, probability of an event can change from experiment to experiment but in probability we always take 0.5 as the probability of getting an even number in a single throw of a die or in more.

Note: Students should take care while using probability. Empirical probability is an experimental event which completely depends upon the experiment. Results of which can differ from day to day but probability is a theoretical event and hence results remain the same.