"Either/Or" Probability for Non-Overlapping Events

1. "Or" Probability for Non-Overlapping Events

When finding "either/or" probability for non-overlapping events, we need to consider the two parts of this term. "Either/or" refers to a scenario in which either one or both of two events happen. However, non-overlapping means they can't both happen at the same time; therefore, exactly one of them happens: either event A OR event B, but not both A and B.

EXAMPLE

Suppose you have a standard deck of 52 cards. You have two mutually exclusive, or non-overlapping, events, like selecting a 6 and selecting a face card. These events can't both happen at the same time. If you are selecting a 6, then you are not selecting a face card, and vice versa.


What's the probability of selecting a 6 or a face card?

Well, there are four 6's and 12 face cards, so 16 out of 52.



It would appear, then, that for non-overlapping events, you can calculate the "or" probability as the individual probabilities added together.

formula to know

Either/Or Probability for Non-Overlapping Events

It is important to note, however, that this formula doesn't work if you have overlapping events.

EXAMPLE

Referring back to our deck of cards, what is the probability of a 6 or diamond?

If you counted out all the cards that were either 6's or diamonds, you would end up with 16 out of 52 cards. However, that's not the same as adding the probability of a 6 (four out of 52) with the probability of a diamond (13 out of 52), which would give you 17 out of 52.



This formula only works for non-overlapping events.

term to know

Either/Or Probability for Non-Overlapping Events

The probability that either of two non-overlapping events occurs is the sum of their individual probabilities. Also known as the "special addition rule."