Multiplication rule
The multiplication rule determines a combined count or probability by multiplying the numbers of choices or the relevant probabilities at successive stages.
Statistics Every Programmer Needs
The multiplication rule of counting determines the number of outcomes formed by successive choices by multiplying the numbers of options at each stage.
- How it is used
- Counts combined outcomes and supplies success and total-outcome counts for theoretical probabilities.
- How deep it goes
- Defines the product formula, works through dice and repeated-position counts, and flags independent choices and changing options.
- Examples
- Uses ordered dice rolls, license plates, three-digit locks, and a Python calculation of 5³ = 125.
- What you can do after
- Apply it to count combined outcomes and calculate probabilities from successful and total outcome counts.
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Grokking Machine Learning
A rule stating that the probability of independent events occurring together equals the product of their individual probabilities.
- How it is used
- Uses joint probabilities to calculate spam-detection probabilities from email features.
- How deep it goes
- Works through conditional probabilities with an email tree and applies independence to estimate joint word probabilities.
- Examples
- Calculates email probabilities using spam, ham, and the words “lottery” and “sale.”
- What you can do after
- Evaluate joint email probabilities and estimate them using an independence assumption.
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Related concepts
- large language modelused by · A large language model is a neural language model trained on extensive text data to process and generate language.
- independenceuses · Two events or random quantities are independent when knowing the outcome or value of one does not change the probability or distribution of the other.
- addition rulecontrasts with · The addition rule determines the total count or probability of mutually exclusive alternatives by summing their individual counts or probabilities.
- Bayesian networkused by · A Bayesian network is a probabilistic graphical model whose directed acyclic graph represents random variables and their conditional dependencies.
- binomial distributionused by · A binomial distribution is the probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success.
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