A probability distribution is a mathematical function that describes the likelihood of different outcomes in a random experiment. It gives us a comprehensive description of how probabilities are distributed over the values of a random variable. There are various types of probability distributions, including discrete distributions (like the binomial distribution) and continuous distributions (like the normal distribution).
A binomial distribution, on the other hand, is a specific type of probability distribution that applies to situations where there are a fixed number of independent trials, each with two possible outcomes (commonly referred to as ‘success’ and ‘failure’). For example, flipping a coin a certain number of times is a scenario that can be modeled by a binomial distribution. The binomial distribution is characterized by two parameters: the number of trials (n) and the probability of success on each trial (p).
In summary, while a probability distribution is a broad concept that encompasses various types of distributions, a binomial distribution is a specific case within that concept, defined by its own rules and characteristics associated with binary outcomes.