Concept of Probability

The following table and graph illustrate the relative frequencies of heads observed when a single coin is repeatedly tossed:
Number of Tosses
Number of Heads
Relative Frequency
Number of Tosses 100 200 300 400 500 600 700 800 900 1000 Number of Heads 46 102 146 203 257 302 346 402 451 502 Relative Frequency 0.46 0.51 0.49 0.51 0.51 0.5 0.49 0.5 0.5 0.5
From the graph, it can be observed that as the number of coin tosses increases, the relative frequency of heads approaches a constant value of .

This limiting value of corresponds to the probability of heads when tossing a fair coin (where the likelihood of heads and tails is equal). Mathematically, this can be expressed as:

In general, when a certain experiment or observation is repeated multiple times, and each possible outcome is equally likely, the relative frequency of an event stabilizes around a constant value. This value equals the ratio of the number of cases where event occurs to the total number of possible outcomes.

This ratio is called the probability of event . The probability of event , denoted as , is given by: