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Probabilistic Independence
“Two events can occur together while leaving each other's probabilities unchanged.”
01 / SUMMARY
In short
A and B are independent if learning one does not change the probability of the other; equivalently, P(A∩B)=P(A)P(B). This is a property of the model or process, not a visual impression.
03 / SCENE
In the wild
Across two fair coin tosses, the first result does not change the probability of heads on the second.
04 / LIMIT
The limit
Independent does not mean mutually exclusive; positive-probability events that exclude each other are dependent.
FINAL NOTE
What remains
Check the product rule or conditional probability instead of trusting intuition.