Fair coin

A fair coin is a coin that, when flipped, has an equal probability of landing on either of its two faces, typically referred to as "heads" and "tails." This means the probability of obtaining heads is 0.5 (or 50%), and the probability of obtaining tails is also 0.5 (or 50%).

The concept of a fair coin is a fundamental idealization used extensively in probability theory, statistics, and game theory. It serves as a simplified model for random events where two outcomes are equally likely. While real-world coins may exhibit slight biases due to imperfections in their shape, weight distribution, or the flipping mechanism, the assumption of fairness is often employed for analytical convenience.

The fairness of a coin can be statistically assessed through experiments involving multiple flips. If, over a large number of flips, the observed frequencies of heads and tails are approximately equal, it provides evidence supporting the coin's fairness. However, even a statistically fair coin can produce streaks of heads or tails due to the inherent randomness of the process.

The fair coin model is used to illustrate various probabilistic concepts, such as:

• Independent events: Each coin flip is independent of previous flips; the outcome of one flip does not influence the outcome of subsequent flips.
• Expected value: The expected number of heads (or tails) in a series of flips is half the total number of flips.
• Binomial distribution: The probability of obtaining a specific number of heads (or tails) in a given number of flips can be calculated using the binomial distribution.
• Hypothesis testing: Coin flips can be used to test hypotheses about probabilities and randomness.

In summary, a fair coin represents a simple yet powerful model for understanding randomness and probability, characterized by its equal chances of landing on either of its two sides.