Which statement best describes marginal probability?

• A. The probability of a single event occurring within the sample space
• B. The probability of the intersection of two events
• C. The probability of the union of two events
• D. The probability that an event B occurs given A

Answer: (A)

Marginal probability is the likelihood of a single event when you look at that one outcome within the entire sample space and ignore any other variables. For a simple die, the probability of rolling a 4 is a marginal probability: it's just the chance of that specific outcome, 1/6.

When two variables are involved, the marginal probability of one value is found by summing the joint probabilities over all possible values of the other variable. In formula form, P(X = 4) = sum over all y of P(X = 4, Y = y). This “summation out” of the other variable leaves you with the probability of the single event X = 4, regardless of what Y did.

This contrasts with the probability of both events happening (the intersection), the probability that either event happens (the union), or the probability of one event given that another has occurred (conditional probability). The marginal probability ignores those dependencies and focuses on one outcome within the entire sample space.