Equally Likely Outcomes
In probability, an experiment can yield outcomes that are said to be equally likely when each outcome has an identical chance of occurring. For example, when tossing a coin, the results can be either Head or Tail, each with a probability of
\[ P(Head) = P(Tail) = \frac{1}{2} \]
Similarly, when rolling a fair die, each number from 1 to 6 has the same probability:
\[ P(n) = \frac{1}{6}, \text{ for } n = 1, 2, 3, 4, 5, 6 \]
As more repetitions of an experiment are performed, the results tend to stabilize around their expected probabilities. The section illustrates how conducting a larger number of tosses results in counts of heads and tails that tend to converge, indicating that these outcomes are equally likely. The concept is foundational in linking the practical outcomes of random experiments to the theoretical framework of probability.