ABSTRACT

The mathematical properties of P(A), the probability of event A, are deduced from the following postulates governing the assignment of probabilities to the elements of a sample space, S.

() P ( S ) = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429124754/be33da89-95f5-45e7-a067-f2fa13b8eb97/content/eq136.tif"/>

P(A) ≥ 0 for any event A

If A 1 , … , A n , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429124754/be33da89-95f5-45e7-a067-f2fa13b8eb97/content/eq137.tif"/> … are mutually exclusive, then() P ( A 1 + A 2 + ⋯ + A n + ⋯ ) = P ( A 1 ) + P ( A 2 ) + ⋯ + P ( A n ) + ⋯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429124754/be33da89-95f5-45e7-a067-f2fa13b8eb97/content/eq138.tif"/>