http://www.ck12.org Chapter 3. An Introduction to Probability
What we have demonstrated is that the probability of the union of two events,AandB, can be obtained by adding
the individual probabilities ofAandBand subtractingP(A∩B). The Venn diagram above illustrates this union.
Formula (1) above is called theAdditive Rule of Probability.
Additive Rule of Probability
The union of two events,AandB, can be obtained by adding the individual probabilities ofAandBand subtracting
P(A∩B). The Venn diagram above illustrates this union.
P(A∪B) =P(A)+P(B)−P(A∩B)
We can rephrase the definition as follows: The probability that either eventAor eventBoccurs is equal to the
probability that eventAoccursplusthe probability that eventBoccursminusthe probability that both occur.
Example:
Consider the experiment of randomly selecting a card from a deck of 52 playing cards. What is the probability that
the card selected is either a spade or a face card?
Solution:
Our event is
E={the card selected is either a spade or a face card}The eventEconsists of 22 cards; namely, 13 spade cards and 9 face cards that are not spade. Be careful, if we say
that we have 12 face cards, we would be over counting the face-spade cards!
To findP(E)we use the additive rules of probability. First, let
C={card selected is a spade}
D={card selected is a face card}