Which distribution defines the probability of successes in a series of trials?

The binomial distribution is the correct choice because it specifically models the number of successes in a fixed number of independent trials, each with the same probability of success. This distribution is particularly useful in situations where one is interested in counting the number of occurrences of a particular event, such as flipping a coin a certain number of times and determining how many times it lands on heads.

In a binomial distribution, there are two possible outcomes for each trial: success or failure. The outcomes are mutually exclusive, and the trials are independent, meaning the outcome of one trial does not affect the outcome of another. The formula for the binomial distribution incorporates the number of trials, probability of success on each trial, and the number of successes desired, making it versatile for various applications, including quality management and process improvement.

The normal distribution, while it can approximate the binomial distribution under certain conditions (specifically when the number of trials is large and the probability of success is neither very close to 0 nor 1), does not define the success in discrete trials. The exponential distribution primarily describes the time between events in a Poisson process and is not concerned with counting successes. The log-normal distribution is related to multiplicative processes and applies to variables that are positively