MathBench > Probability

Laws of AND and OR

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.

musselsSo 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 get '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 quahog settlements (in other words, hard surface). Furthermore, assume that only 2% of clams survive on sand, while 20% of clams 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%







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