Probability Probability is the frequency of a particular outcome occurring across a number of trials 𝑝 𝐴 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑐𝑙𝑎𝑠𝑠𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑎𝑠 𝐴 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

Outcome Types Equally Likely Model – all outcomes are equally likely of occurring Mutually Exclusive Outcomes – outcome of one trial is independent of the outcome on any other trial

Theorems for Probability Addition Theorem: 𝑝 𝐴 𝑜𝑟 𝐵 =𝑝 𝐴 +𝑝(𝐵) Multiplication Theorem: 𝑝 𝐴 𝑎𝑛𝑑 𝐵 =𝑝 𝐴 ∗𝑝(𝐵)

Probability and Inference Probabilities are theoretical They are expectations of what will happen Actual trials are empirical They are actually what does happen