Transcript Probability

Probability & Sample
Space
Probability
The probability of a number is a ratio that
compares the number of successes to
the total possible outcomes.
number of successes
P(E) =
number of possible outcomes (sample space)
Probability
Probabilities can be expressed as a fraction,
a decimal, or a percent.
0%
50%
100%
0
Impossible
1/2
1
Certain
Probability
Something that will never happen has a 0%
probability.
Exmaple: There is a 0% probability that humans will be able
to breath underwater (without an oxygen mask).
0%
50%
0
Impossible
1/2
100%
1
Certain
Probability
Something that will always happen has a 100%
probability.
Example: There is a 100% probability that water will freeze
At 32 degrees Fahrenheit.
0%
50%
100%
0
Impossible
1/2
1
Certain
Sample Space
In order to determine the probability of an
event occurring, you must first
determine the sample space.
The sample space of an event is all
possible outcomes.
Example 1
Suppose your favorite color
is teal.
If you were going to close
your eyes and choose a
balloon at random, what is
the probability that you
would choose your
favorite color?
Example 1
First we must determine the
sample space:
There are four possible
outcomes: you could grab
the peach one, the purple
one, the pink one, or the
teal one.
Example 1
The sample space is all
possible outcomes:
Peach
Purple
Pink
Teal
Example 1
The probability of grabbing the
teal balloon is the number of
teal balloons, 1, divided by
the number of possible
outcomes, 4.
P(teal) =
1
4
Example 1
We can also find the probabilities
for the other colors.
P(peach) =
P(purple) =
P(pink) =
1
4
1
4
1
4
Example 2
You are playing a game that involves one
die. What is the probability of rolling a
6?
First we must determine the sample
space.
Example 2
The sample space
is all possible
outcomes:
1, 2, 3, 4, 5, and 6.
Example 2
So the probability of
rolling a 6 is:
1
6
Example 3
Suppose you were going to roll a
tetrahedral die. What is the probability
of rolling a 1?
Sample Space: 1, 2, 3, 4
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Example 3
Since there are only four outcomes, the
The probability of rolling a 1 is:
1
4
Example 4
Suppose you were
going to toss two
coins. What is the
sample space?
HH
HT
TH
TT
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Example 4
What is the
probability of
tossing two heads?
HH
HT
TH
TT
1
4
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Example 4
What is the
probability of
tossing two tails?
HH
HT
TH
TT
1
4
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QuickTi me™ and a
T IFF (Uncom pressed) decom pressor
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Example 4
What is the
probability of
tossing a head and
a tail?
HH
HT
TH
TT
2 1

4 2
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Example 5
You are playing a game that involves 2
dice. What is the sample space?
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Example 5
On the first die,
we can get a 1,
2, 3, 4, 5, or 6.
On the second
die, we can get
a 1, 2, 3, 4, 5, or
6.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Example 5
So the sample space is:
Example 5
Since there were six possible numbers we
could roll for the first die, and six
possible numbers we could roll for the
second die,
there are a total of 6 x 6 = 36 possible
combinations!
Example 6
You are going to buy a pizza. The pizzas
come in three different sizes with three
choices of seasoning.
Size
Seasoning
Small
Pepper
Medium
Basil
Large
Onions
Example 6
What is the sample space?
Let’s use a counting tree to
help us determine all the
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can create!
Example 6
So the sample space is:
Small + Pepper
Small + Basil
Small + Onion
Medium + Pepper
Medium + Basil
Medium + Onion
Large + Pepper
Large + Basil
Large + Onion
There were 3 choices for the
size, and 3 choices for the
seasoning.
So there are a total of 3 x 3 = 9
possible combinations!
Example 7
A restaurant offers 5
main entrees, 7 side
items, and 6
beverages.
How many different
meals are possible?
Entree
Side
Beverage
Steak
Potatoes
Coffee
Chicken
Squash
Hot Tea
Shrimp
Beans
Iced Tea
Salmon
Carrots
CocaCola
Pork
Peas
Sprite
Okra
Milk
Spinach
Example 7
For each meal, you
must choose an
entrée, a side, and a
beverage.
So there are
5 x 7 x 6 = 210
different possible
meals.
Entree
Side
Beverage
Steak
Potatoes
Coffee
Chicken
Squash
Hot Tea
Shrimp
Beans
Iced Tea
Salmon
Carrots
CocaCola
Pork
Peas
Sprite
Okra
Milk
Spinach