Probability Theory Concepts
2 concepts · Grades 9-12
This family view narrows the full statistics map to one connected cluster. Read it from left to right: earlier nodes support later ones, and dense middle sections usually mark the concepts that hold the largest share of future work together.
Use the graph to plan review, then use the full concept list below to open precise pages for definitions, examples, and related content.
Concept Dependency Graph
Concepts flow left to right, from foundational to advanced. Hover to highlight connections. Click any concept to learn more.
Connected Families
Probability Theory concepts have 4 connections to other families.
All Probability Theory Concepts
Law of Large Numbers
As the number of trials increases, the experimental probability (sample average) converges to the theoretical probability (population mean).
"Flip a coin 10 times: maybe 7 heads (70%). Flip 100 times: closer to 50%. Flip 10,000 times: very close to 50%. More trials = more reliable averages. Short-run luck evens out."
Why it matters: LLN justifies using samples to estimate population parameters. It's why insurance, casinos, and polling work.
Expected Value
The long-run average outcome of a random process, calculated as the sum of each outcome times its probability.
"If you played a game forever, expected value is your average result per play. Positive EV = profitable long-term. Negative EV = you'll lose over time. It's the mathematical way to evaluate risky decisions."
Why it matters: Expected value is the foundation of rational decision-making under uncertainty. It's used in gambling, insurance, investment, and game theory.