Single Word Frequency Likelihood

In computational linguistics and natural language processing, understanding how frequently individual words appear in a text collection is a fundamental building block for many language models. The unigram model treats each word as an independent event, computing the probability of any word based solely on its relative frequency in the corpus—ignoring any contextual dependencies between words.

This concept forms the foundation of language modeling, where we estimate the probability distribution over sequences of words. By computing the likelihood of isolated words (unigrams), we establish the simplest probabilistic model of language, which serves as a baseline for more sophisticated n-gram and neural language models.

Sentence Boundary Markers: In language modeling, it is essential to model where sentences begin and end. We use special tokens to mark these boundaries:

• <s> — Start-of-sentence marker
• </s> — End-of-sentence marker

These markers are treated as regular tokens when computing probabilities, allowing the model to learn patterns about sentence structure and length distributions.

Computing Word Likelihood: Given a corpus represented as a space-separated string of tokens (including boundary markers), the likelihood of a specific word is calculated as:

$$P(word) = \frac{\text{count}(word)}{\text{total tokens in corpus}}$$

Your Task: Implement a function that calculates the probability of a given word appearing in a corpus of tokenized sentences. Your implementation should:

• Tokenize the corpus by splitting on whitespace
• Count the occurrences of the target word
• Divide by the total number of tokens (including <s> and </s> markers)
• Return the probability rounded to 4 decimal places