Bifalgorithm post · Brisk · Chapter 1

Why is this not a valid probability measure?

Why is this not a valid probability measure? (Brisk · Chapter 1) — "I told you that Pr({Ben})=.1, Pr({Chad})=.2, Pr({Grover})=.3, and Pr({Tim})=.3. Would you b…

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  • The listed values do not define a valid probability measure.
  • The claimed probabilities are Pr({Ben}) = .1, Pr({Chad}) = .2, Pr({Grover}) = .3, and Pr({Tim}) = .3.
  • The probabilities of all outcomes must sum to Pr(Ω) = 1.
  • The claimed probabilities sum to .9.
  • Because .9 is not equal to 1, the probability measure is invalid.
  • The claim should not be believed.
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Why is this not a valid probability measure?

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Brisk

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"I told you that Pr({Ben})=.1, Pr({Chad})=.2, Pr({Grover})=.3, and Pr({Tim})=.3. Would you believe me? Better not. This is not a valid probability measure, since the sum of the probabilities of all the outcomes, Pr( Ω ), is not equal to 1."

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