# Probability theory

Probability theory is the mathematics governing quantitative degrees of belief.

Children:

- Well-calibrated probabilities
Even if you’re fairly ignorant, you can still strive to ensure that when you say “70% probability”, it’s true 70% of the time.

- Bayesian reasoning
A probability-theory-based view of the world; a coherent way of changing probabilistic beliefs based on evidence.

- Odds
Odds express a relative probability.

- Mutually exclusive and exhaustive
The condition needed for probabilities to sum to 1

- Probability
The degree to which someone believes something, measured on a scale from 0 to 1, allowing us to do math to it.

- Normalization (probability)
That thingy we do to make sure our probabilities sum to 1, when they should sum to 1.

- Sample space
The set of possible things that could happen in a part of the world that you are uncertain about.

- Probability distribution (countable sample space)
A function assigning a probability to each point in the sample space.

- Square visualization of probabilities on two events
- Two independent events
What do pair of dice, pair of coins, and pair of people on opposite sides of the planet all have in common?

- Probability distribution: Motivated definition
People keep writing things like P(sick)=0.3. What does this mean, on a technical level?

Parents:

- Mathematics
Mathematics is the study of numbers and other ideal objects that can be described by axioms.

- Rationality