Table of Contents

• 1: Introduction
• The Law of OR
• 2: All Life's a Game
• 3: The Law of OR
• 4: Some Fine Print
• 5: What if you violate the fine print?
• The Law of AND
• 6: More game shows
• 7: What are the chances?
• 8: The Law of AND
• 9: More Fine Print
• 10: Examples of independent events
• 11: What if you violate the fine print?
• AND and OR together
• 12: Summary
• 13: Practice with dice
• 14: Practice with coins
• Biological Applications
• 15:What else can probability do?
• 16: To Curl or not to Curl
• 17: Surviving the Numbers Game
• 18: Gaining an Edge
• 19: Hanging on for Dear Life

More Fine Print ... this time the Law of AND

In order for the Law of AND to work, the two events have to be independent. What does that mean? It means that one event does not influence the other. The fact that one event has occurred does not make the other more likely.

For example, getting hurt and going to the hospital are NOT independent events. My chances of getting hit on the head by a falling tree this year are maybe 1 in a hundred, or 1%. My chances of going to the emergency room this year are maybe also 1%. So using the Law of AND, my chances of getting hit in the head and going to the hospital would be 1% × 1% = 0.01 × 0.01 = 0.0001 = 0.01%, or one-hundreth of a percent.

But in fact, IF I get hit in the head, I'm likely to want to go to the hospital for that very reason. So, the two events are NOT independent!! And my chances of getting hit in the head and going to the hospital are much bigger than 0.01%. Maybe more like 0.5% (about half the time that I get hit in the head I go to the hospital).

My street after the last tropical storm -- luckily I did not get hit by this falling tree!