Probability is how machine learning talks about uncertainty. Instead of saying what will happen with certainty, a model can express how likely a result is and how confident we should be in a decision.## Core Ideas| Concept | Meaning | Business example || --- | --- | --- || $P(A)$ | probability of an event | probability a customer buys || $P(A \mid B)$ | probability given evidence | probability of churn given low engagement || $E[X]$ | expected value | average payoff of a campaign || Variance | uncertainty around the average | stability of a KPI |mermaidflowchart LR A[Define event] --> B[Estimate probability] --> C[Update with evidence] --> D[Choose action]Alt text: Probability estimates a chance, updates it with evidence, and informs a decision.## Worked Example 1If 25 of 100 visitors purchase, then:

## Worked Example 2Bayes’ rule updates belief when new evidence arrives:

For example, it can tell us how likely a customer is high-value given that they opened a premium offer email.## Guided Practice1. What does $P(A \mid B)$ mean?2. Why is expected value useful in business?3. Why can a high expected value still be risky?