Theory:

In grade \(9\), we learned the concept of empirical probability. Let us recall.
Empirical probability or experimental probability is defined as the number of times an event has occurred to the total number of times an experiment is performed.
Let us consider an example.
Example:
On throwing a die of \(6\) faces \(100\) times, the frequencies of the outcomes are as follows:
 
Face \(1 = 18\), Face \(2 = 10\), Face \(3 = 37\), Face \(4 = 5\), Face \(5 = 13\), Face \(6 = 17\).
 
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Based on this experiment, the empirical probability of face \(1\) is \(\frac{18}{100}\) i.e. \(0.18\)
 
Similarly, the empirical probability of face \(2\) is \(\frac{10}{100} = 0.1\).
 
The empirical probability of face \(3\) is \(0.37\), face \(4\) is \(0.05\), face \(5\) is \(0.13\) and face \(6\) is \(0.17\).
In the eighteenth century, French naturalist Comte de Buffon tossed a coin \(4040\) times and got \(2048\) heads. The experimental probability of getting a head, in this case, was \(\frac{2048}{4040}\), i.e., \(0.507\). J.E. Kerrich, from Britain, recorded \(5067\) heads in \(10000\) tosses of a coin. The experimental probability of getting a head, in this case, was \(\frac{5067}{10000} = 0.5067\). Statistician Karl Pearson spent some more time making \(24000\) tosses of a coin. He got \(12012\) heads, and thus, the experimental probability of a head obtained by him was \(0.5005\).
 
In general, the empirical probability of a head seems to settle down around the number \(0.5\), i.e., \(\frac{1}{2}\), which is called as theoretical probability.
 
Let us discuss the concept of theoretical probability in the upcoming sessions.