The probability of only 2 possible outcomes - For instances- a student randomly guessing the answers to 25 multiple-choice is the example of

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BlackTom AI · Accepted Answer

Let's restate the problem to be clear: The scenario describes a student randomly guessing answers to 25 multiple-choice questions, where each question has two possible outcomes (correct or incorrect) for each guess. The question asks which probability distribution models this situation best.

Option 1: Poisson distribution. The Poisson distribution is typically used for counting the number of events in a fixed interval when events are rare and occur with a low probability, especially as an approximation to a binomial when n is large and p is small. Here, we have a finite number of trials (25 questions) with two outcomes per trial, not a rare-event count scenario. Thus Poisson is not the most natural fit for this setup.

Option 2: Binomial distribution. The binomial distribution describes the number of successes in n independent Bernoulli trials, each with the same probability of success p. In our case, each guess is a Bernoulli trial with a probability of success (getting a question right) of p = 0.5 if randomly guessing on a typical 4- or 5-option MCQ, and there are n = 25 independent trials. This exactly matches the binomial framework for counting how many correct answers occur.

Option 3: Uniform distribution. The uniform distribution assigns equal probability to a range of outcomes. It is not the correct model for counting the number of correct answers in a fixed number of trials, because the binomial distribution accounts for the discrete count of successes, not a flat probability over all possible counts of successes.

Option 4: Hypergeometric distribution. The hypergeometric distribution models draws without replacement from a finite population containing a certain number of successes and failures. Our guessing scenario treats each question as an independent trial with replacement (the probability of success remains the same for each guess). Since there’s no dependence created by removing questions after each guess, hypergeometric is not appropriate here.

In summary, among the listed distributions, the one that best captures the number of correct guesses in 25 independent Bernoulli trials with a constant success probability is the binomial distribution, because it directly models the count of successes in a fixed number of independent trials with two outcomes per trial.

The probability of only 2 possible outcomes - For instances- a student randomly guessing the answers to 25 multiple-choice is the example of

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