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Probability of Independent and
you should learn
Find the probability
Two events are
if the occurrence of one has no effect on the
of independent events.
occurrence of the other. For instance, if a coin is tossed twice, the outcome of the
first toss (heads or tails) has no effect on the outcome of the second toss.
Find the probability
of dependent events, as
applied in Ex. 33.
P R O BA B I L I T Y O F I N D E P E N D E N T E V E N T S
you should learn it
If A and B are independent events, then the probability that both A and B occur
To solve real-life
is P(A and B) = P(A) • P(B).
problems, such as finding
the probability that the
Florida Marlins win three
games in a row in
Probability of Two Independent Events
E X A M P L E 1
You are playing a game that involves spinning the
money wheel shown. During your turn you get to
spin the wheel twice. What is the probability that
you get more than $500 on your first spin and then
go bankrupt on your second spin?
Let event A be getting more than $500
on the first spin, and let event B be going bankrupt
on the second spin. The two events are independent.
So, the probability is:
P(A and B) = P(A) • P(B) =
. . . . . . . . . .
The formula given above for the probability of two independent events can be
extended to the probability of three or more independent events.
Probability of Three Independent Events
E X A M P L E 2
During the 1997 baseball season, the Florida Marlins won 5 out of 7
home games and 3 out of 7 away games against the San Francisco Giants. During the
1997 National League Division Series with the Giants, the Marlins played the first
two games at home and the third game away. The Marlins won all three games.
Estimate the probability of this happening.
Source: The Florida Marlins
Let events A, B, and C be winning the first, second, and third games.
The three events are independent and have experimental probabilities based on the
regular season games. So, the probability of winning the first three games is:
P(A and B and C) = P(A) • P(B) • P(C) =
Chapter 12 Probability and Statistics