Mutually exclusive event
Mutually exclusive events are events that cannot occur simultaneously and have no outcomes in common.
Statistics Every Programmer Needs
A mutually exclusive event is an event that cannot occur simultaneously with another event in the same set of alternatives.
- How it is used
- Uses mutually exclusive alternatives to calculate the probability of either event through the addition rule.
- How deep it goes
- Defines simultaneous impossibility, gives the addition formula, and contrasts it with multiplication for independent events.
- Examples
- Uses die outcomes, alternative reading choices, travel routes, and choosing between a coin flip and die roll.
- What you can do after
- Apply the addition rule to calculate probabilities for alternatives that cannot occur simultaneously.
Read how Statistics Every Programmer Needs explains mutually exclusive event →
Math and Architectures of Deep Learning
Events that cannot occur together because their pairwise intersections are empty.
- How it is used
- Organizes discrete or continuous outcomes so probability distributions and their normalization can be expressed correctly.
- How deep it goes
- Defines empty pairwise intersections, relates them to union probabilities, and extends the sum rule from sums to integrals.
- Examples
- Uses Statsville weight ranges and infinitesimal intervals as discrete and continuous examples.
- What you can do after
- Evaluate whether events overlap and apply probability addition when events are mutually exclusive.
Read how Math and Architectures of Deep Learning explains mutually exclusive event →
Related concepts
- addition ruleuses · The addition rule determines the total count or probability of mutually exclusive alternatives by summing their individual counts or probabilities.
- eventaddresses · An event is a specified occurrence or set of outcomes in a probability model whose occurrence can be evaluated or assigned a probability.
- sum ruleused by · The normalization rule stating that the total probability over all possible outcomes equals one.
- independencecontrasts with · 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.
- set intersectionequivalent to · Set intersection is the set of elements that belong to every one of two or more sets.
- eventkind of · An event is an occurrence, change, or associated record or notification recognized as significant within a system or context.
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