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

Hanging on for dear life

(Last in a series of three)

In aquatic environments, many juvenile animals get passively carried along in the current and since their ability to swim is so weak, they essentially have no control over where they land. But, where they land will have a big influence over whether or not they survive.

So the question is, what is the overall probability of survival for such an animal? A mussel, for instance. Let's make it simple and assume that the poor guy only gets 'picked up' and transported once in his life. At the end of this possibly involuntary roller-coaster of a ride, he will get deposited on either a good hard surface into which he can sink his byssal threads, or shifting sand, which will (usually) quickly smother him.

Assume that only 15% of the bottom is suitable for mussel settlements (in other words, hard surface). Furthermore, assume that only 2% of mussels survive on sand, while 20% of mussels survive on hard substrate. What is our guy's overall chance of survival?

Once again, please try to figure out what information above will lead to a mathematical solution.

 

There are two ways for this critter to survive: land on sand and survive, OR land on a hard surface and survive:

P(survival) =

P((land on sand AND survive on sand) OR (land on rock AND survive on rock)) =

0.85 × 0.02 + 0.15 × 0.20 =

0.017 + 0.030 = 0.047, or about 5%

 

Summary

In this module you have:

• Investigated  the differences between mutually exclusive events and independent events, and
• Calculated probabilities associated with each type of event

 

 

 

 

 

If you want a printer-friendly version of this module, you can find it here in a Microsoft Word document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.