The OR rule

The general concept: The OR rule is applied when you want to know the probability that any one of a specified set of outcomes has occurred. This arises in questions such as:

• What is the probability that you roll either a 4 or a 5 on a die?
• What is the probability that you roll an even number on a die?
• What is the probability that you draw a King from a deck of cards?
• What is the probability that a child has either red or brown hair?
• What is the probability that either of two children has red hair?

Sometimes the set of outcomes you have to take into consideration is obvious. For example, you may be asked to calculate the probability that, if you roll a 6-sided dice you get a 1 or a 2. Other times you may have to do a bit of work to figure out what set of outcomes you are being asked about. For example, say you roll one die (with 6 sides) and want to know the probability that it will be an even number. A moment of thought will lead you to realize that what you want to know is the probability that the outcome is any number from the set {2, 4, 6}. If you want to know the probability that it is a number less that 5 then it is any outcome from the set {1, 2, 3, 4}. It is not uncommon to have to take a minute to figure out the set you need to work with before proceeding to the application of the rule as discussed next.

The Basic and the Non-exclusive OR: We are going to make a distinction between what we will call the Basic OR and what we will call the Non-Exclusive OR. Not everybody does this; the Basic OR is really just a subset of what we will be calling the Non-Exclusive OR and so many people will define the OR in the way that we define the Non-Exclusive OR. Once we have discussed them we will look at how the two rules are related to one another and why the Basic OR is a subset of the other.

The distinction between them is that the Basic OR applies when the set of outcomes you are interested in are mutually exclusive while the non-exclusive OR applies when they are NOT mutually exclusive. This difference will be covered in more detail in the individual pages.

The reason I break down the OR rule into two parts is that the Basic OR is used far more frequently, particularly in the area of genetics that we are covering, and it is easier to learn. The Non-Exclusive OR will come up on occasion in it’s most simple form and so it is not a bad thing to take it into consideration only in these rare cases and to apply the Basic OR everywhere else.

Details on each are on these individual pages:

• The Basic OR


• The Non-Exclusive OR