Which distribution is illustrated by trials where each trial has two possible outcomes?

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The Binomial distribution is appropriate for scenarios where there are a fixed number of trials, each having two possible outcomes, commonly referred to as "success" and "failure." This distribution models the number of successes in a set number of independent Bernoulli trials.

Each trial is conducted under the same conditions, meaning the probability of success remains constant throughout all trials. For example, if you were flipping a coin a certain number of times, the Binomial distribution could model the number of heads (successes) obtained. The characteristics of having a specific number of trials and the binary outcome make the Binomial distribution a fundamental concept in probability theory and statistics.

The other distributions mentioned do not fit this description as closely. The Normal distribution deals with continuous outcomes and is used for large sample sizes due to the Central Limit Theorem. The Geometric distribution models the number of trials until the first success occurs, rather than a fixed number of trials. The Poisson distribution is applicable for modeling the number of events occurring within a fixed interval of time or space, particularly when these events happen independently of each other.

Thus, the Binomial distribution is the correct answer since it perfectly aligns with the conditions of having multiple independent trials and only two possible outcomes for each