Addition Rule
The addition rule is used in probability and statistics to calculate the probability that an event “A” or “B” happens — either individually or both at the same time. For example, you might wish to calculate your probability of getting a parking ticket if you’re unable to find a parking spot and have to park illegally, or you might want to find your probability of buying a winning lottery ticket and that ticket being the jackpot ticket. Set notation is usually used to calculate using the addition rule:P(A∪B) = P(A)+P(B)-P(A∩B)
What this is saying in English is the probability of event A OR event B happening (or both at the same time) is the probability of event A happening on its own, plus the probability of event B happening on its own, plus the probability of both events happening at the same time.
- P(A)=probability that event A occurs
- P(B)=probability that event B occurs
- P(A∪B) = probability that either event A or event B occurs
- P(A∩B) = probability that event A and event B happen at the same time.
There are a couple of useful facts that you can use with the addition rule:
- If it isn’t logically possible for the events to occur together (called “mutually exclusive”) then P(A∩B)=0. In this case, the addition rule just becomes P(A∪B) = P(A)+P(B).
- If the events have no influence on each other (“independent events”) then the addition rule becomes P(A∪B) = P(A)+P(B)-P(A)*P(B)).
A mutually exclusive event is one where there’s no chance of things happening together. For example, you can’t parachute out of an airplane if you never fly in planes, you can’t win the lotto if you don’t buy a ticket and you can’t get a speeding ticket if you never drive. Independent events have no influence on each other. For example, winning the lotto and finding that lost sock the dryer at, or getting a speeding ticket and a parking ticket on the same day.
