Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
The multiplication rule for probability
Apply conditional product rules and interpret joint-event probabilities
Problem types
- The multiplication rule
Builds on
- Finding a conditional probability
- Multiplying fractions
- The binomial theorem · Useful idea
The probability of exactly k successes in n independent trials multiplies the success probabilities and a binomial coefficient.
- Independence and mutual exclusion · Earlier idea
For independent events the conditional probability equals the ordinary probability, so the joint probability is a product.
Leads to
- A distribution from a sample space · Extend the idea
Multiplying the probabilities along a sequence of trials gives the probabilities in a theoretical distribution.
- Comparing uncertain strategies · See it applied
Along a decision tree, probabilities multiply along each path to find the chance of each payoff.
- Checking a chance model by simulation · See it applied
A simulation of repeated independent trials is compared with the product of probabilities.
Related skills
- Arc length and sector area · Shared foundations
- Using expected value to compare choices · Shared foundations
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