Classifying Events

1
Chapter 8 Probability
8.2A
Classifying Events
MATHPOWERTM 12, WESTERN EDITION
8.2A.1
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Independent Versus Dependent Events
Two events are independent if the probability
that each event will occur is not affected by the
occurrence of the other event.
Two events are dependent if the outcome of the
second event is affected by the occurrence of the
first event.
Classify the following events as independent or
dependent
a) tossing a head and rolling a six
independent
b) drawing a face card, and not returning it to
the deck, and then drawing another face
card
dependent
c) drawing a face card and returning it to the
deck, and then drawing another face card
independent
If the probabilities of two events are P(A) and
P(B) respectively, then the probability that
both events will occur, P(A and B), is
P(A and B) P(A) x P(B)
8.2A.2
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Finding Probability

• A cookie jar contains 10 chocolate and 8 vanilla
  cookies.
• If the first cookie drawn is replaced, find
  the probability of

a) drawing a vanilla and then a chocolate cookie
P(V and C) P(V) x P(C)
The probability of drawing a vanilla and a
chocolate cookie is
b) drawing two chocolate cookies
P(C and C) P(C) x P(C)
The probability of drawing two chocolate cookies
is
8.2A.3
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Finding Probability

• Find the probability of drawing a vanilla and
  then drawing a
• chocolate cookie, if the first cookie drawn
  is eaten.

P(V and C) P(V) x P(C)
The probability of drawing a vanilla and a
chocolate cookie is 0.2614.
3. An aircraft has three independent computer
guidance systems. The probability that each
will fail is 10-3 . What is the probability
that all three will fail?
P(all three fail) P(A) x P(B) x P(C)
10-3 x 10-3 x 10-3 10-9
The probability that all three will fail is 10-9.
8.2A.4
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Probability
The sum of all the probabilities of an event is
equal to 1.
If P 1, then the event is a certainty.
If P 0, then the event is impossible.
In probability, if Event A occurs, there is also
the probability that Event A will not occur.
Event A not occurring is the compliment of Event
A occurring.
The probability of Event A not occurring is
written as P(A). (This is read as Probability of
not A).
For Event A P(A) P(A) 1

P(A) 1 - P(A)
Example One card is drawn from a deck of 52
cards. What is the probability of each of these
events? a) drawing a red four b) not drawing
a red four
8.2A.5
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Finding the Probability of the Same Birth Month
In a group of seven people, what is the
probability that at least two have their
birthdays in the same month?
Find the probabilities of the seven birthdays
being in seven different months.
1st person
5th person
2nd person
6th person
3rd person
7th person
4th person
P(birthdays in 7 different months)
0.111
P(at least 2 birthdays in the same month) 1 -
(different months) 1 -
0.111 0.889
8.2A.6
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Finding the Probability of the Same Birth Month
contd
P(birthdays in 7 different months)
0.111
P(at least 2 birthdays in the same month) 1
0.111
0.889
Alternative Method
12 x 11 x 10 x 9 x 8 x 7 x 6 can be expressed
as 12P7.
12 x 12 x 12 x 12 x 12 x 12 x 12 can be
expressed as 127.
P(birthdays in 7 different months)
0.111
P(at least 2 birthdays in the same month)
0.889
8.2A.7
8
Assignment
Suggested Questions Pages 380 and 381 1-6, 14,
16, 17 ab
8.2A.8
9
Chapter 8 Probability
8.2B
Exclusivity
8.2B.9
MATHPOWERTM 12, WESTERN EDITION
10
Classifying Exclusivity
Two events are mutually exclusive if they cannot
occur simultaneously.
For instance, the
events of drawing a diamond and drawing a club
from a deck of cards are mutually exclusive
because they cannot both occur at the same time.
For mutually exclusive events
P(A or B) P(A) P(B)
Events that are not mutually exclusive have some
common outcomes.
For instance, the events of
drawing a diamond and drawing a king from a deck
of cards are not mutually exclusive because the
king of diamonds could be drawn, thereby having
both events occur at the same time.
For events that are not mutually exclusive
P(A or B) P(A) P(B) - P(A and B)
8.2B.10
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Classifying Exclusivity
Classify each event as mutually exclusive or not
mutually exclusive.
a) choosing an even number and choosing a prime
number
not mutually exclusive
b) picking a red marble and picking a green
marble
mutually exclusive
c) living in Edmonton and living in Alberta
not mutually exclusive
d) scoring a goal in hockey and winning the game
not mutually exclusive
e) having blue eyes and black hair
not mutually exclusive
8.2B.11
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Probability and Exclusivity
1. A box contains six green marbles, four white
marbles, nine red marbles, and five black
marbles. If you pick one marble at a time,
find the probability of picking
a) a green or a black marble.
P(G or B) P(G) P(B)
b) a white or a red marble.
P(W or R) P(W) P(R)
8.2B.12
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Probability and Exclusivity
2. Determine the probability of choosing a
diamond or a face card from a deck of
cards.
P(D or F) P(D) P(F) - P(D and F)
The probability of choosing a diamond or a face
card is
8.2B.13
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Probability and Exclusivity
3. A national survey revealed that 12.0 of
people exercise regularly, 4.6 diet
regularly, and 3.5 both exercise and diet
regularly. What is the probability that a
randomly-selected person neither exercises
nor diets regularly?
Find the probability that a person exercises or
diets regularly.
P(D or F) P(D) P(F) - P(D and F)
0.12 0.046 - 0.035
0.131
Therefore, the probability that a person
neither exercises nor diets regularly is
1 - 0.131 0.869
86.9
8.2B.14
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Probability and Exclusivity contd
Alternative method Use a Venn diagram
A national survey revealed that 12.0 of
people exercise regularly, 4.6 diet
regularly, and 3.5 both exercise and diet
regularly. What is the probability that a
randomly-selected person neither exercises
nor diets regularly?
Entire Population
Dieter
Exerciser
3.5
1.1
8.5
Therefore, the probability that a person
neither exercises nor diets regularly is
100 - (8.5 3.5 1.1) 86.9
8.2B.15
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Assignment
Suggested Questions Pages 380 and 381 7-13, 15,
18, 20
8.2B.16