How does the binomial distribution model the number of heads in repeated coin tosses?

In probability and statistics, the binomial distribution models the number of successes (e.g., "heads") in a fixed number of independent trials where each trial has only two possible outcomes.12

To model coin tosses, the experiment must satisfy four conditions:
* Fixed trials: The coin is tossed a specific number of times, denoted as n.12
* Binary outcomes: Each toss results in either "success" (heads) or "failure" (tails).13
* Constant probability: The probability of heads, denoted as p, remains the same for every toss.12
* Independence: The outcome of any single toss does not affect the others.12

The binomial distribution provides the probability of obtaining exactly x heads in n tosses. Mathematically, this is determined by the kth term in the expansion of the binomial expression $(p+q{)}^n$, where $q=1-p$. This framework allows statisticians to calculate the likelihood of specific outcomes—such as the probability of getting exactly two heads in ten tosses—by applying the binomial probability mass function.12