Dr. J introduces the mathematical definition of probability.

An experiment is any data collection process. A particular result of an experiment is an outcome. The collection of all possible outcomes is the sample space of the experiment. Any subset of the sample space is an event.

Probability is a function of an event. By Kolmogorov's axioms of probability: 1) this function is a non-negative real number, 2) the probability of the sample space is 1, and 3) the probability of the union of pairwise disjoint set is the sum of their probabilities.

Conditional probability of B given A can be calculated by calculating the probability of the intersection of B and A and dividing by the probability of A.

- Slides: [ Ссылка ]

00:24 - Experiments and Events
03:07 - Probabilities for rolling 6-sided dice
05:12 - Kolmogorov's Axioms of Probability
08:10 - Visualizing probability
08:56 - Visualizing Kolmogorov's 3rd axiom
09:55 - Revisiting probabilities for rolling 6-sided dice
13:38 - Consequences of Kolmogorov's axioms
16:09 - Conditional probability
17:44 - Visualizing conditional probability
18:42 - Conditional probability: die rolling
20:11 - Summary

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