Advanced Deep Learning with Python

Probability and sets

The collection of all possible outcomes (events) of an experiment is called, sample space. We can think of the sample space as a mathematical set. It is usually denoted with a capital letter and we can list all the set outcomes with {} (the same as Python sets). For example, the sample space of coin toss events is S_c = {heads, tails}, while for dice rows it's S_d = {1, 2, 3, 4, 5, 6}. A single outcome of the set (for example, heads) is called a sample point. An event is an outcome (sample point) or a combination of outcomes (subset) of the sample space. An example of a combined event is for the dice to land on an even number, that is, {2, 4, 6}.

Let's assume that we have a sample space S = {1, 2, 3, 4, 5} and two subsets ...