Editing Probability axioms (section)

== Simple example: coin toss ==
Consider a single coin-toss, and assume that the coin will either land heads (H) or tails (T) (but not both).  No assumption is made as to whether the coin is fair or as to whether or not any bias depends on how the coin is tossed.<ref>{{cite journal |last1=Diaconis |first1=Persi |last2=Holmes |first2=Susan |last3=Montgomery |first3=Richard |title=Dynamical Bias in the Coin Toss |journal= SIAM Review|date=2007 |volume=49 |issue=211–235 |pages=211–235 |doi=10.1137/S0036144504446436 |bibcode=2007SIAMR..49..211D |url=https://statweb.stanford.edu/~cgates/PERSI/papers/dyn_coin_07.pdf |access-date=5 January 2024}}</ref>

We may define:

: <math>\Omega = \{H,T\}</math>
: <math>F = \{\varnothing, \{H\}, \{T\}, \{H,T\}\}</math>

Kolmogorov's axioms imply that:

: <math>P(\varnothing) = 0</math>
The probability of ''neither'' heads ''nor'' tails, is 0.

: <math>P(\{H,T\}^c) = 0</math>
The probability of ''either'' heads ''or'' tails, is 1.

: <math>P(\{H\}) + P(\{T\}) = 1</math>
The sum of the probability of heads and the probability of tails, is 1.