7.3 Combining Probabilities

When probabilities are combined, as with our lottery example above, the probabilities are multiplied together to determine the final probability for the combined events. The rules of Boolean Algebra are used to combine probabilities (4).

The two most commonly used Boolean Algebra terms are the logical “AND” and “OR.” When two probabilities are combined using AND logic, as with our lottery example, the two probabilities are multiplied together.

Winning the first lottery AND winning the second lottery:

In an accident analysis our events might appear something like:

Another example would be:

A probability can be associated with the event and then combined to develop an overall probability for the event.

The probability associated with a driver running a red light might be 1/1000 red lights or 0.001. The probability associated with the cross street driver not being able to stop might be 1/100 or 0.01. Combining these two probabilities yields the overall probability of an accident occurring because of the two events:

The logical “OR” is used when several events can occur, but only one of these events can lead to an outcome. For instance, an accident can occur if any of the following events occur:

In this case, the probabilities are added instead of multiplying

The structure of fault trees use these basic logical terms in their construction. This will be explained in detail in Chapter 14.