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

Surviving the numbers game

Many animals have hundreds, thousands, or even tens of thousands of babies. You can bet that these offspring are not being doted on, spoiled, or gifted with designer jeans. Nope! In fact, their parents expect most of them to die.

For example, the sphinx moth lays up to 1000 eggs on the underside of leaves. In one (fictional) experiment, 327 out of 500 eggs survived to hatching. In a second experiment, 7 out of 70 caterpillars survived to become adult moths. Given this information, what is the likelihood that any given egg will survive to adulthood?

Surviving to adulthood implies that the egg survived to become a caterpillar AND the caterpillar survived to become an adult moth. So,

P(survival to adulthood) =
P(egg → caterpillar) * P(caterpillar → adult)

	Just what are these probabilities? Based on the information above, 327 out of 550 eggs survived to caterpillarhood, i.e., P(egg → cpillar) = 327 / 500 = 0.654
	Likewise, P( cpillar → adult) = 7 / 70 = 0.1
	So, P(egg → adult) = 0.654 * 0.1 = 0.065.