Understanding Basic Probability Is The First Step To Better Models

Before ChatGPT could write essays, explain tax code, or summarize earnings reports, it had to master something far simpler but no less profound: probability. While headlines may credit “artificial intelligence” or “deep learning” for recent breakthroughs, the unsung hero behind it all is basic statistics. Specifically, a foundational concept every high school student learns but few realize powers the future of computing: Bayes’ Theorem.

In this article, I’ll demystify how conditional probability underpins large language models, and explain why this concept is just as vital for detecting financial fraud or customer churn as it is for generating human-like text.

The Math That Predicts Your Next Word

At its core, a LLM is a machine that tries to predict the next most probable word in a sentence. Just as a financial analyst might assess the probability that a customer will default on a loan, a LLM constantly calculates the likelihood of the next word given the context so far.

That’s where conditional probability enters the picture. The notation P(A|B), read as “the probability of A given B,” is central to both. In finance, this might translate to, “What’s the probability this transaction is fraudulent, given it occurred at 3 AM and originated from an unusual location?” In natural language processing, the question becomes, “What’s the probability the next word is ‘bank’ given the sentence so far is ‘She walked into the’?”

To answer these questions, both disciplines rely on joint probabilities and Bayes’ Theorem, which help update our beliefs as new data comes in.

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From Classroom Examples to Language Models

Let’s revisit the basics, using an example from the above machine learning lecture. Imagine a classroom where 60% of students passed the first test. Of those who passed, 80% passed a second test. But among those who failed the first, only 30% passed the second. We can calculate not only joint probabilities (e.g. the chance of passing both tests is 0.6 × 0.8 = 0.48) but also conditional probabilities, such as the chance someone passed Test 1 given they passed Test 2.

Now swap “tests” with “tokens” (the basic building blocks of language models), and you’ll see the parallel. LLMs are built on probabilistic trees just like this, calculating and updating the likelihood of word combinations based on vast amounts of training data.

What Bayes’ Theorem Has to Do With Netflix, Fraud, and Forecasting

Bayes’ Theorem is particularly useful when we know the outcome but want to infer the cause. This is a common task in both NLP and finance.

Take Netflix. Suppose 65% of users who watched Star Wars also watched Return of the Jedi. Among those who didn’t watch Star Wars, only 45% watched Return of the Jedi. Given that a user has watched Return of the Jedi, Bayes’ Theorem helps calculate the probability they’ve also watched Star Wars. This kind of reverse inference is the same logic your bank uses when flagging suspicious activity.

For instance, imagine your institution has found that 1% of transactions are fraudulent. Bayes’ Theorem helps determine, if a transaction meets certain risk conditions (e.g. high value, unusual location), what’s the updated probability that it’s fraudulent?

The formula is:

P(Fraud∣RiskConditions)=P(RiskConditions∣Fraud)⋅P(Fraud)P(RiskConditions)P(Fraud|RiskConditions) = \frac{P(RiskConditions|Fraud) \cdot P(Fraud)}{P(RiskConditions)}P(Fraud∣RiskConditions)=P(RiskConditions)P(RiskConditions∣Fraud)⋅P(Fraud)​

Even if the base fraud rate is low, a sharp rise in the conditional likelihood given new evidence can make the system flag the transaction.

Why This Matters for Financial Services

Financial services companies aren’t just passive observers of machine learning. They’re deeply invested in using these tools for credit scoring, fraud detection, customer segmentation, and product personalization.

1. Credit Risk Modeling

Banks traditionally rely on credit bureaus and fixed rules to determine whether to issue a loan. But these rules often fall short for gig workers, immigrants, or small businesses without long credit histories. By layering in conditional probabilities, such as the likelihood of repayment given nontraditional income sources, models become more inclusive and predictive.

2. Fraud Detection

As mentioned earlier, conditional probability allows firms to update risk assessments in real-time. A single unusual transaction may not be enough to trigger an alert. But if it happens at 3 AM in a foreign country, and the cardholder has never traveled there, the combined joint probability might cross a critical threshold.

3. Churn Prediction

Telecom and banking industries also rely on these models to predict customer churn. If 4% of users typically leave each month, but that rate jumps to 20% for those who call customer service twice in a week and reduce spending, conditional models help flag these high-risk customers in time for retention efforts.

Building LLMs: It’s All Just Scaled-Up Probability

So, how do LLMs take these fundamental ideas and scale them up to billions of parameters?

Training a language model involves feeding it massive datasets—entire libraries of text—and calculating the probability of each word given the preceding ones. These models build probabilistic maps between tokens (words or characters), fine-tuned using gradient descent and backpropagation. But at every stage, the fundamental mechanism remains the same: “Given X, what’s the probability of Y?”

Just as financial institutions use structured data (like transaction logs) and unstructured data (like call transcripts or emails) to make predictions, LLMs blend grammar, syntax, and semantics to forecast text.

It All Comes Back to Bayes

Whether you’re training an LLM to draft SEC filings or building a fraud model for a neobank, the math is the same. Bayes’ Theorem helps us reverse-engineer cause from effect. Joint probability teaches us to calculate combined outcomes. And conditional probability lets us make intelligent decisions when new information arises.

In a world increasingly driven by data and algorithms, mastering these simple principles isn’t just for data scientists. It’s essential for any executive leading digital transformation.

Because whether you’re predicting credit defaults or chatbot responses, the future still runs on the math you learned in high school.

If you too want to learn more about this, consider the ‘No Code AI and Machine Learning: Building Data Science Solutions Program’ delivered by MIT through the Great Learning platform, use this link for $100 off.

For more on this topic on Forbes, check out: ‘How AI, Data Science, And Machine Learning Are Shaping The Future’ or ‘AI’s Growing Role In Financial Security And Fraud Prevention’.