Conditional probability measures how likely event A is when event B is known to occur. Unlike unconditional probability P(A), P(A|B) incorporates information about B. Bayes’ rule relates the two conditional probabilities: P(A|B) = P(B|A)P(A) / P(B). section 12.2
Height and professional basketball
For a randomly selected person, the probability of being over six feet tall is about 7%. Given that the person is a professional basketball player, it rises to about 99%. Reversing the condition, Bayes’ rule combines the basketball-player base rate, the 7% height rate, and the 99% conditional rate to estimate a 0.0000193 probability that someone over six feet plays professional basketball. section 12.2
Bayes’ rule uses these probability inputs:
- P(A): the unconditional probability of the target event. section 12.2
- P(B): the unconditional probability of the observed condition. section 12.2
- P(B|A): the condition’s probability when the target event is known. section 12.2
