The Handy Math Answer Book

tain event has caused an observed outcome by using estimates for all possible out-
comes. Its simplest notation is as follows:

What are mutually exclusive events?

Mutually exclusive events are those that are impossible to occur together. For exam-
ple, a subject in a study of male and female humans can’t be both male and female.
Males are males; females are females. Thus, depending on what the study is about
(such as a study of how many males versus females go to college from a certain high
school), both “events” will be mutually exclusive.

What are the addition rulesof probability?

In probability theory, the addition rule is used to determine the probability of events A
or Boccurring. The notation is most commonly seen in terms of sets: P (AB) P
(A) P (B) P (AB), in which P (A) represents the probability that event Awill occur,
P (B) represents the probability that event Bwill occur, and P (AB) is translated as
the probability that event Aor event Bwill occur. For example, if we wanted to find
the probability of drawing a queen (A) or a diamond (B) from a card deck in a single
draw, and since we know there are 4 queens and 13 diamond cards in the deck of 52,
the equation and resulting probability becomes: 4/52 13/52 1/52 16/52 (the
1/52 is derived by multiplying 4/52 13/52).

()

()

()

PA B ()()

PB

PA B

PB

^h==+:PPABA

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APPLIED MATHEMATICS

How is set theory used to represent the relationships among events?

S

tatisticians often use the set theory to represent relationships among events

(collections of outcomes of an experiment). This is usually written in the fol-

lowing notation, in which Aand Bare two events in the sample space S:

• AB, or “either Aor Boccurs, or both”; this is said as “A union B” in set
  theory;


• AB, or “both Aand Boccur”; this is said as “A intersection B” in set
  theory;


• AB, or “if Aoccurs, so does Boccur”; this is said as “A is a subset of B” in
  set theory;


• A', or “Adoes not occur.”