3.3 The Addition Rule

Report
Statistics Notes
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In the previous section, you learned how to
find the probability of two events, A and B,
occurring in sequence. Such probabilities are
denoted by P(A and B). (ex – flipping a heads
and rolling a 3)
In this section, you will learn how to find the
probability that at least one of two events will
occur. Probabilities such as these are denoted
by P(A or B) and depend on whether the
events are mutually exclusive.
Two events A and B are
mutually exclusive if A
and B cannot occur at
the same time.
 The Venn diagrams
show the relationship
between events that
are mutually exclusive
and events that are not
mutually exclusive.
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1.
Event A: Roll a 3 on a die.
Event B: Roll a 4 on a die.
2.
Event A: Randomly select a male student.
E vent B: Randomly select a nursing major.
3.
Event A: Randomly select a blood donor
with type “0” blood.
Event B: Randomly select a female blood
donor.
1.
Event A: Randomly select a jack from a standard
deck of cards
Event B: Randomly select a face card from a
standard deck of cards
2.
Event A: Randomly select a 20 -year.- old student.
Event B: Randomly select a student with blue eyes.
3.
Event A: Randomly select a vehicle that is a Ford.
Event B. Randomly select a vehicle that is a Toyota.
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Addition Rule 1
 If events A and B are mutually exclusive, then the
rule can be simplified to
 P(A or B) = P(A) + P(B)
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This simplified rule can be extended to any
number of mutually exclusive events.
Addition Rule 2
 The probability that events A or B will occur P(A or
B) is given by
 P(A or B) = P(A) + P(B) - P(A and B).
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A box contains 3 glazed doughnuts, 4 jelly
doughnuts, and 5 chocolate doughnuts. If a
person selects a doughnut at random, find
the probability that it is either a glazed
doughnut or a chocolate doughnut.
P(glazed or chocolate)= P(glazed) + P
(Chocolate)= 3/12 + 5/12 = 8/12 = 2/3
The events are Mutually Exclusive.
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At a political rally, there are 20 Republicans,
13 Democrats, and 6 independents. If a
person is selected at random, find the
probability that he or she is either Democrat
or Republican.
P(Democrat or Independent)= P(Democrat) +
P(Independent)
=13/39 + 6/39 =19/39
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A day of the week is selected at random. Find
the probability that it is a weekend day.
P(Saturday or Sunday) = P(Saturday) +
P(Sunday)
P(Saturday or Sunday) = 1/7 + 1/7 = 2/7
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A single card is drawn at random from an
ordinary deck of cards. Find the probability
that it is either an ace or a black card.
P(ace or black card) = P(ace) + P(black card)
P(ace or black card) = 4/52 + 26/32 – 2/52 =
28/52 = 7/13
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In a hospital units there are 8 nurses and 5
physicians; 7 nurses and 3 physicians are
female. If a staff person is selected, find the
probability that the subject is a nurse or a
male.
P(nurse or male) = P(nurse) + P(male)
P(nurse or male) = 8/13 + 3/13 – 1/13= 10/13
On New Year’s Eve, the probability of a person
driving while intoxicated is 0.32 the probability
of a person having a driving accident is 0.09, and
the probability of a person having a driving
accident while intoxicated is 0.06. What is the
probability of a person driving while intoxicated
or having a driving accident?
 P(intoxicated or accident) = P(intoxicated) + P (
accident) – P(intoxicated and accident)
 =.32 + 0.09 – 0.06= 0.35
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The frequency
distribution shows the
volume of sales (in
dollars) and the number
of months a sales
representative reached
each sales level during
the past three years. If
this sales pattern
continues, what is the
probability that the sales
representative will sell
between $75,000 and
$124,999 next month?

Find the probability
that the sales
representative will sell
between $0 and
$49,999.

A blood bank catalogs the
types of blood, including
positive or negative Rh-factor,
given by donors during the
last five days. The number of
donors who gave each blood
type is shown in the table. A
donor is selected at random.
 Find the probability that the
donor has type 0 or type A blood.
 Find the probability that the
donor has type B blood or is Rhnegative.
 Find the probability that the
donor has type B or type AB
blood.
 Find the probability that the
donor has type O blood or is
Rh-positive.

Use the graph at the
right to find the
probability that a
randomly selected
draft pick is not a
running back or a wide
receiver.

Find the probability
that a randomly
selected draft Pick is
not a linebacker or a
quarterback.

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