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Glacius
ProbabilityConcept reference

Probability assignments

A finite probability assignment has nonnegative outcome masses summing to one.

1 min read1 figureSources & further reading
On this page 7 sections
  1. Overview
  2. A finite probability assignment gives each outcome a mass
  3. To fill one missing mass, subtract the known total from 1
  4. Zero masses are allowed
  5. Key takeaway
  6. Sources & further reading
  7. Concept connections

01A finite probability assignment gives each outcome a mass#

A finite probability assignment gives each outcome a mass. Every mass must be nonnegative, and the masses of the complete sample space must add to 1.

For A, B and C, masses 0.2, 0.3 and 0.5 pass both tests. The outcomes do not need equal masses.

Outcomes A,B,C have nonnegative masses .2,.3,.5. Their proportional segments exactly fill a strip of total probability 1.Outcomes A,B,C have nonnegative masses .2,.3,.5. Their proportional segments exactly fill a strip of total probability 1.
Figure 1Outcomes A,B,C have nonnegative masses .2,.3,.5. Their proportional segments exactly fill a strip of total probability 1.
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Check your reasoning

Masses: 0.3, 0.3, 0.3. Check the assignment.

  1. AValid.
  2. BInvalid: unequal.
  3. CInvalid: total 0.9.
Show answer and explanation
Invalid: total 0.9.

Their total is 0.9.

02To fill one missing mass, subtract the known total from 1#

To fill one missing mass, subtract the known total from 1. If two masses are 0.2 and 0.6, they use 0.8, leaving 0.2.

Check your reasoning

A model returns exactly one of A, B, C. Their masses are 0.1, 0.6, ?. Find the missing mass.

Show answer and explanation
0.3

The missing mass is 1 − 0.7 = 0.3.

03Zero masses are allowed#

Zero masses are allowed. Negative masses are not: −0.1, 0.4 and 0.7 total 1 but still fail. Checking only the total misses this error.

Check your reasoning

Masses: -0.1, 0.2, 0.9. A learner says “total 1, so valid.” Correct?

  1. AValid: total 1.
  2. BInvalid: negative.
  3. CInvalid: unequal.
Show answer and explanation
Invalid: negative.

−0.1 is negative.

Key takeaway

Check every mass and the complete total. Unequal masses and zero masses are allowed; negative masses and a total other than one fail.

Sources & further reading

  1. [1]

Reference this concept

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

Glacius. “Probability assignments.” Math behind ML. /learn/p-axioms