Final Answer:
The probability of success for the Bernoulli random variable X with p = 0.25 is 0.25.
Step-by-step explanation:
In probability theory, a Bernoulli random variable is associated with a binary outcome, often referred to as success or failure. The parameter p represents the probability of success. In this scenario, where p = 0.25, it means that there is a 25% chance of success.
Mathematically, the probability mass function (PMF) of a Bernoulli random variable is given by P(X = x) = p^x * (1 - p)^(1-x), where x is the outcome (0 for failure, 1 for success). Since we are interested in the probability of success, x = 1. Substituting this into the PMF with p = 0.25, we get P(X = 1) = 0.25^1 * (1 - 0.25)^(1-1) = 0.25, which is the probability of success.
Understanding the probability parameter p is essential for interpreting the characteristics of a Bernoulli distribution. In this case, the final answer, 0.25, denotes the likelihood of observing a success for the given Bernoulli random variable X.