But there are also rules of addition for
mutually exclusive and independent
events. For mutually exclusive events, or
events that can’t occur together, the addi-
tion rule reduces to P (AB) P (A) P
(B). For independent events, or those that
have no influence on each other, the addi-
tion rule reduces to P (AB) P (A) P
(B) P (A) | P (B).What are the multiplication rules
of probability?
In probability theory, the multiplication
rule is used to determine the probability
that two events, Aand B,both occur. As
with the addition rules, the notation for
multiplication rules of probability are
most commonly seen in terms of sets:
P(AB) P(A|B) •P(B) or P(AB) P(B|A) •P(A), 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 Aand event Bwill both
occur. In addition, P(A|B) is the conditional probability that event Aoccurs given that
event Bhas already occurred, and P(B|A) is the conditional probability that event B
occurs given that event Ahas already occurred. Similar to the addition rules, if there
are independent events (or those that have no influence on one another), the equation
reduces to P(AB) P(A) •P(B).What is the law of total probability?
The law of total probability can be written as follows: The probability that an event A
will occur, P(A), is equal to the probability that event Aand event Bboth occur, plus
the probability that event Aand event B' occur (or Aoccurs and Bdoes not). Using the
multiplication rule, this is written as:
P(A) P(A|B) •P(B) P(A|B') •P(B')What was the “gambler’s ruin”?
The gambler’s ruin is an application of the law of total probability that was first pro-
posed by Dutch mathematician and astronomer Christiaan Huygens (1629–1695),
although many people before him, including astronomer Galileo Galilei (1564–1642),
252 brought up the same probability problem, but phrased it differently. By 1656, Huygens
Skilled card players have developed mathematical
skills that help them estimate the chances of which
cards might be held by their opponents based on what
has been played and dealt already. Stone/Getty Images.