Which distribution is characterized by a fixed probability of success in each trial?

Which distribution is characterized by a fixed probability of success in each trial?

• A. The normal distribution
• B. The geometric distribution
• C. The uniform distribution
• D. The Bernoulli distribution

Answer: (B)

The distribution that is characterized by a fixed probability of success in each trial is the Bernoulli distribution. This distribution models a single trial that can have one of two possible outcomes: a success or a failure. In the context of a Bernoulli trial, the probability of success remains constant across each trial, typically denoted by \( p \), while the probability of failure is \( 1 - p \). The geometric distribution, although related, actually describes the number of trials needed to achieve the first success in a series of independent Bernoulli trials. While it still centers around the concept of fixed probability, it specifically focuses on the count of trials rather than a single trial, which leads to a different application. The normal distribution, by contrast, is used for modeling continuous variables and does not deal with fixed probabilities in trials. The uniform distribution represents outcomes that are equally likely but does not relate to success or failure in trials. Thus, the Bernoulli distribution is the appropriate selection since it directly addresses the concept of a fixed probability of success in a single trial setting.

The distribution that is characterized by a fixed probability of success in each trial is the Bernoulli distribution. This distribution models a single trial that can have one of two possible outcomes: a success or a failure. In the context of a Bernoulli trial, the probability of success remains constant across each trial, typically denoted by ( p ), while the probability of failure is ( 1 - p ).

The geometric distribution, although related, actually describes the number of trials needed to achieve the first success in a series of independent Bernoulli trials. While it still centers around the concept of fixed probability, it specifically focuses on the count of trials rather than a single trial, which leads to a different application. The normal distribution, by contrast, is used for modeling continuous variables and does not deal with fixed probabilities in trials. The uniform distribution represents outcomes that are equally likely but does not relate to success or failure in trials.

Thus, the Bernoulli distribution is the appropriate selection since it directly addresses the concept of a fixed probability of success in a single trial setting.