Oil Spills. The U.S. Coast Guard maintains a database of the...

Oil Spills. The U.S. Coast Guard maintains a database of the number, source, and location of oil spills in U.S. navigable and territorial waters. The following is a probability distribution for location of oil spill events. [SOURCE: Statistical Abstract of the United States] $$\begin{array}{l|c} \hline \text { Location } & \text { Probability } \\ \hline \text { Atlantic Ocean } & 0.008 \\ \text { Pacific Ocean } & 0.037 \\ \text { Gulf of Mexico } & 0.233 \\ \text { Great Lakes } & 0.020 \\ \text { Other lakes } & 0.002 \\ \text { Rivers and canals } & 0.366 \\ \text { Bays and sounds } & 0.146 \\ \text { Harbors } & 0.161 \\ \text { Other } & 0.027 \\ \hline \end{array}$$ Apply the special addition rule to find the percentage of oil spills in U.S. navigable and territorial waters that a. occur in an ocean. b. occur in a lake or harbor. c. do not occur in a lake, ocean, river, or canal.

Oil Spills. The U.S. Coast Guard maintains a database of the number, source, and location of oil spills in U.S. navigable and territorial waters. The following is a probability distribution for location of oil spill events. [SOURCE: Statistical Abstract of the United States]
$$\begin{array}{l|c}
\hline \text { Location } & \text { Probability } \\
\hline \text { Atlantic Ocean } & 0.008 \\
\text { Pacific Ocean } & 0.037 \\
\text { Gulf of Mexico } & 0.233 \\
\text { Great Lakes } & 0.020 \\
\text { Other lakes } & 0.002 \\
\text { Rivers and canals } & 0.366 \\
\text { Bays and sounds } & 0.146 \\
\text { Harbors } & 0.161 \\
\text { Other } & 0.027 \\
\hline
\end{array}$$
Apply the special addition rule to find the percentage of oil spills in U.S. navigable and territorial waters that
a. occur in an ocean.
b. occur in a lake or harbor.
c. do not occur in a lake, ocean, river, or canal.

Key Concepts

Probability Distribution

A probability distribution is a mathematical function that describes the likelihood of occurrence of different outcomes in an experiment. It assigns a probability to each outcome, ensuring that the sum of all probabilities equals one. In this context, it provides a framework to understand how oil spill events are distributed across various locations.

Special Addition Rule

The special addition rule is used to determine the probability that at least one of several mutually exclusive events will occur. For events that cannot happen at the same time, this rule states that the total probability is simply the sum of their individual probabilities. This rule is essential when calculating combined probabilities for events like oil spills occurring on different isolated bodies of water.

Mutually Exclusive Events

Mutually exclusive events are events that cannot occur simultaneously. In probability, when dealing with mutually exclusive events, the probability of either event happening is calculated by adding the probabilities of each event, as there is no overlap. This concept is crucial when determining the overall probability for non-overlapping categories of events.

Complement Rule

The complement rule in probability states that the probability of an event not occurring is equal to one minus the probability that it does occur. This concept is useful when it is easier to calculate the probability of the occurrence of an event and then subtract it from one to obtain the probability of the event’s complement, such as oil spills not happening in certain designated areas.

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