Summary
Highlights
The human brain is exceptionally good at recognizing patterns, sometimes even when they don't exist, a phenomenon called pareidolia. This natural inclination to see patterns extends to sequences of events, which is where the concept of probability becomes relevant.
Statisticians define two types of probability: empirical and theoretical. Empirical probability is observed from actual data and provides an estimate. Theoretical probability is an ideal truth that we try to approximate using empirical data, much like estimating population parameters from a sample.
The addition rule helps calculate the probability of one event OR another occurring. For mutually exclusive events (those that cannot happen at the same time), the probability of A or B is simply the sum of their individual probabilities. Notation P(Event) is introduced.
When events are not mutually exclusive (they can happen at the same time), the full addition rule is used: P(A or B) = P(A) + P(B) - P(A and B). This subtracts the overlap to avoid double-counting, as visually represented by a Venn Diagram.
The multiplication rule helps calculate the probability of two or more things happening at the same time. For independent events (where the occurrence of one does not affect the other), P(A and B) = P(A) * P(B). An example of meeting Cole Sprouse and getting free ice cream is used.
Conditional probability, written as P(Event 1 | Event 2), is the probability of one event occurring given that another event has already happened. If events are independent, P(Event 1 | Event 2) equals P(Event 1). Conditional probabilities are crucial in medical screenings, helping to understand the true likelihood of a condition given a test result, highlighting differences between P(Cancer|Positive Test) and P(Positive Test|Cancer).
While exact probabilities are often hard to calculate in daily life, understanding probability helps set realistic expectations, make informed decisions, and understand the likelihood of various outcomes in diverse situations, from college applications to catching illnesses.