Probability Day 01

Rules probability must follow

• The probability that nothing occurs is 0
• The probability that something occurs is 1
• The probability of something is 1 minus the probability that the opposite occurs
• The probability of at least one of two (or more) things that cannot simultaneously occur (mututally exclusive) is the sum of their respective probabilities
• If an event A implies the occurence of event B, then the probability of A occuring is less than the probability that B occurs
• For any two events the probability that at least one occurs is the sum of their probabilities minus their intersection.

References
Brian Caffo, Jeff Leek and Roger D. Peng, Statistical Inference Lecture Notes, Johns Hopkins Bloomberg School of Public Health, coursera.org, 2015