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Glacius
ProbabilityConcept reference

Events

An event is a subset of a sample space and occurs when the observed outcome belongs to it.

1 min read1 figureSources & further reading
On this page 7 sections
  1. Overview
  2. An event is a subset of the sample space
  3. Events can select records by several features
  4. The empty subset describes no qualifying outcome
  5. Key takeaway
  6. Sources & further reading
  7. Concept connections

01An event is a subset of the sample space#

An event is a subset of the sample space. It occurs when the observed outcome belongs to that subset.

For S = {1, 2, 3, 4}, “greater than 2” selects 3 and 4. Either observed result makes the event occur.

The whole sample space S contains 1, 2, 3 and 4. Its subset A, the outcomes greater than 2, contains exactly 3 and 4. Outcomes 1 and 2 are outside A but inside S.The whole sample space S contains 1, 2, 3 and 4. Its subset A, the outcomes greater than 2, contains exactly 3 and 4. Outcomes 1 and 2 are outside A but inside S.
Figure 1The whole sample space S contains 1, 2, 3 and 4. Its subset A, the outcomes greater than 2, contains exactly 3 and 4. Outcomes 1 and 2 are outside A but inside S.
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Check your reasoning

S = {1, 2, 3, 4}. Event: result < 3. Choose its subset.

  1. A{1, 2}
  2. B{3, 4}
  3. C{3}
Show answer and explanation
{1, 2}

The qualifying outcomes are {1, 2}.

02Events can select records by several features#

Events can select records by several features. “Red AND square” keeps only records satisfying both conditions. Every included record must already belong to the sample space.

Check your reasoning

Records: u=red/round; v=red/square; w=blue/round. Event: red AND square. Select its IDs.

  1. A{u, v}
  2. B{v}
  3. C{w}
Show answer and explanation
{v}

v is red and square.

03The empty subset describes no qualifying outcome#

The empty subset describes no qualifying outcome. The whole sample space describes all of them. A single outcome, several outcomes, or either boundary can define an event.

Check your reasoning

S = {1, 2, 3}. Event: result ≥ 2. A learner chose {1}. Repair it.

  1. A{1}
  2. B{3}
  3. C{2, 3}
Show answer and explanation
{2, 3}

Keep {2, 3}; both are ≥ 2.

Key takeaway

Translate the event into a membership test. Keep every outcome that passes, including none or all when appropriate.

Sources & further reading

  1. [1]
    Pishro-Nik, Introduction to Probability, 1.3.1 Random Experiments ↗Pishro-Nik, Introduction to Probability · Book

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Events.” Math behind ML. /learn/p-events