Probability

The probability of an event is its value under a probability measure, a real number between zero and one. It compares the mass assigned to that event with the unit mass of the whole sample space. For a finite sample space with equally likely outcomes, $\mathbb{P}(A)=|A|/|\Omega |$. For unequal outcome masses, add their individual probabilities instead.

For example, selecting a coin with head probability $1/2$ with chance $4/5$, or a coin with head probability $3/4$ with chance $1/5$, gives head probability $(4/5)(1/2)+(1/5)(3/4)=11/20$. This is the law of total probability: averaging over the hidden selection is part of calculating the outcome's probability.

Probability is a branch of mathematics that deals with the quantification of uncertainty. It measures how likely an event is to occur, expressed as a number between 0 and 1, or as a percentage between 0% and 100%. Here are some key concepts related to probability: 1. **Experiments and Outcomes**: A probability experiment is a procedure that yields one or more outcomes. An outcome is the result of a single trial of an experiment.