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Using Probability
Mathematics, Grade 7
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Study Guide Using Probability Mathematics, Grade 7
❮
1
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3
❯
USING
PROBABILITY
Probability
is
the
possibility
that
a
certain
event
will
occur.
Probability
is
the
chance
of
an
event
occurring
divided
by
the
total
number
of
possible
outcomes.
Probability
is
based
on
whether
events
are
dependent
or
independent
of
each
other.
•
An
independent
event
refers
to
the
outcome
of
one
event
not
affecting
the
outcome
of
another
event.
•
A
dependent
event
is
when
the
outcome
of
one
event
does
affect
the
outcome
of
the
other
event.
The
number
of
ways
that
an
event
can
happen
depends
on
the
order.
•
A
permutation
is
an
arrangement
of
objects
in
which
order
matters.
•
A
combination
is
a
set
of
objects
in
which
order
does
not
matter.
Just
as
probability
refers
to
the
possibility
of
an
event
happening,
odds
refer
to
the
odds
against
an
event
happening.
How
to
use
probability
The
probability
of
one
event
occurring
is
equal
to
the
chance
of
the
event
occurring
divided
by
the
total
outcomes.
Probabilities
of
independent
or
dependent
events
are
based
on
how
one
event
affects
the
other
event,
if
at
all.
•
For
example,
if
there
are
10
marbles
in
a
bag
with
4
blue
and
6
red
marbles,
the
probability
of
picking
a
red
marble,
putting
it
back
and
then
picking
another
red
marble
is
6/10
·
6/10
=
36/100
or
9/25.
This
probability
is
independent
because
what
happened
the
first
time
does
not
affect
what
happens
the
second
time.
This
can
be
shown
by
the
term
'with
replacement',
which
means
that
the
first
item
has
been
replaced.
The
probability
of
picking
a
red
marble
and
then
another
red
marble
without
replacing
the
first
is
6/10
·5/9
=
30/90
or
1/3.
This
probability
is
dependent
because
the
first
event
affects
the
second
event.
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Permission
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for
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purchaser
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copies
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educational
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Since
probability
is
divided
by
total
outcomes,
it
is
useful
to
be
able
to
figure
out
the
total
outcomes.
Permutations
are
a
way
to
arrange
objects
in
which
order
matters.
•
For
example
if
there
are
3
students
and
3
chairs,
the
way
the
can
be
arranged
is
as
follows:
Ex.
There
are
3
chairs,
___,
___,
___.
There
are
3
students
to
choose
from
for
the
first
chair,
_3_,
___,
___.
There
are
2
students
to
choose
from
for
the
second
chair,
_3_,
_2_,___.
There
is
one
student
left
for
the
last
chair,
3_,
_2_,
_1_.
The
number
of
ways
the
3
students
can
be
arranged
in
3
chairs
is
3
·
2
·
1
or
3!
=
6
ways.
The
notation,
a!,
means
factorial,
which
is
the
product
of
the
consecutive
numbers
from
a
to
1.
A
combination
is
another
way
to
figure
out
total
outcomes,
but
in
the
case
of
combinations,
order
does
not
matter.
For
example,
how
many
different
combinations
can
be
made
when
picking
2
letters
out
of
the
word
DOG?
Ex.
The
combinations
of
two
letters
are:
DO,
DG,
and
OG
Since
order
does
not
matter,
DO
and
OD
are
considered
the
same.
There
are
3
ways
to
pick
2
letters
out
of
the
word
DOG.
Another
concept
with
probability
is
odds.
Odds
refer
to
the
odds
against
an
event
happening.
Odds
are
used
to
compare
unfavorable
possibilities
with
favorable
possibilities.
For
example,
what
are
the
odds
of
picking
a
seven
out
of
a
deck
of
52
cards?
Ex.
There
are
52
-
4
or
48
ways
not
to
get
a
seven.
There
are
4
ways
to
get
a
seven.
The
odds
against
picking
a
seven
are
48:4
The
odds
are
48:4
because
there
are
48
unfavorable
possibilities
compared
to
4
favorable
possibilities.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
Try
This!
1.
What
is
the
probability
of
picking
a
red
card
out
of
a
deck
of
52
cards,
replacing
it
and
then
picking
out
an
ace?
2.
There
are
4
red,
6
yellow
and
5
blue
marbles
in
a
bag.
What
is
the
probability
of
picking
a
red
marble,
and
without
replacing
it,
then
picking
out
a
blue
marble?
3.
How
many
permutations
can
be
made
by
arranging
the
letters
in
the
word,
MATH?
4.
How
many
combinations
can
be
made
from
picking
two
flavors
of
ice
cream
out
of
the
flavors,
strawberry,
vanilla,
chocolate
and
mint?
5.
What
are
the
odds
against
rolling
the
number
5
on
a
die?
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
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