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Independent events leave one another’s probabilities unchanged.
Two events are independent when knowing that one occurred does not change the probability of the other. Under the model of independent tosses of a fair coin, five heads in a row do not make tails more likely on the next toss.
Independence is an assumption to examine, not a property of every repeated event. Drawing an item without replacing it changes what remains and can change the next probability. The useful question is what information or physical conditions the first outcome changes.
A bag holds one red ball and one blue ball. After drawing red without replacement, the next ball must be blue. Those draws are not independent.
Real events may share causes or constraints even when they occur at different times.
Introductory Statistics 2e — Independent and Mutually Exclusive Events
OpenStax contributors · OpenStax, Rice University
CC BY 4.0. Rewritten as a self-contained explanation; the example and reflection are Vakataka additions. Written and edited with AI assistance. No source images reproduced.
Source edition: 2024-12-16T15:08:45Z
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