Probability Portal

1Overview

Probability theory describes uncertain events by a sample space and assigned probabilities. In a finite sample space, one first counts outcomes accurately and then uses those counts to study probability, expected value, conditional probability, and independence.

2Learning sequence

1. Use permutations and combinations to count outcomes while distinguishing whether order matters.
2. Define probability on a finite sample space of equally likely outcomes, and compute expected value as a weighted average.
3. For an event $B$B with $P\left(B\right)>0$P(B)>0, restrict the sample space to $B$B and normalize probabilities by $P\left(B\right)$P(B) to define conditional probability; then distinguish conditional probability from independence.

3Connection to statistics

Probability theory analyzes properties of probabilistic models, whereas statistics infers properties of models or populations from observed data. Probability and expected value are prerequisites for probability distributions and inferential statistics.