Probability Unit
Reference Packet
Probability: is the likelihood or chance of an event occurring.
Sample Space: A set of all possible outcomes in the set
Event: A subset of outcomes within the sample space.
Probability Scale: A scale used to graph the probability of simple events. The scale can
represent probabilities in the form of a fraction, decimal, or percent.
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The probability of an event is a number between 0 and 1.
The greater the probability, the greater the chances the event will happen.
If an event is impossible, the probability that it will occur is 0 or 0%.
If an event is certain to happen, the probability that it will happen is 1 or 100%.
Types of Probability:
Theoretical Probability is what should happen when you perform an experiment.
P(event) 
# of favorable outcomes
total # of possible outcomes
Example: Rolling a number cube.
P (odd ) 
3 1

6 2
Experimental Probability is what happens when you actually perform the event.
P(event) 
Example: Flipping a coin 4 times.
# of times the event occurs
total # of trials
Trial 1
Trial 2
Trial 3
Trial 4
H
T
T
T
P ( heads ) 
1
4
Simulation: an experiment that is designed to model the action in a given situation. They
often use models to act out an event that would be impractical to perform.
Probability Using a Deck of Cards: There are 52 cards in a standard deck of cards.
o Two colors in a deck
o
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26 black cards

26 red cards
Each suit consists of number cards (ace – 10) and face cards:
Suits:
Face cards:
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13 diamonds
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4 Queens
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13 hearts
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4 Kings
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13 spades
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4 Jacks
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13 clubs
Events in probability:
COMPLEMENT OF AN EVENT:
“The chance of all of the other
outcomes”.
Example: What is the probability when rolling a number cube?
The event of this probability is rolling a
The complement of this probability would be the chance
5 or a 6:
of not getting a 5 or 6.
P(5 or 6) =
2
6
1
=3
P(not a 5 or 6) =
4
6
2
=3
Notice the sum of their probabilities equal 1.
P(5 or 6) + P(not 5 or 6) = 1 + 2 = 3 = 1
3 3 3
Compound Events: An event that is made up of two or more simple events
Sample Space: is the set of all possible outcomes in an event or an experiment.
A sample space is written in a list.
Tree Diagram: is an illustration of all of the possible outcomes in an experiment.
Fundamental Counting Principle: states that if one event has m possible outcomes
and a second event has n possible outcomes, then there are mn
total possible outcomes for the two events together.
Example:
Below shows all the possible outcomes for flipping a coin then rolling a number cube.
Tree Diagram
Sample Space
H1
T1
H2
T2
H3
T3
H4
T4
H5
T5
H6
T6
Counting Principle
2 x 6 = 12
The Fundamental
Counting Principle
determines the
number of possible
outcomes (size of
sample space)
Two Types of Compound Events:
1) Independent Events: is when the result of the first event does not affect the result of
the second event.
EXAMPLES:
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Choosing a marble from a jar AND landing on heads after tossing a coin.
Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the second
card.
Selecting one month of the year AND one day of the week.
Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die.
2) Dependent Events: When the result of the first event affects the result of the second
event.
EXAMPLES:
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A money bag contains 2 nickels, a penny, and 4 dimes. A dime is chosen and then, without
replacing the dime, a penny is chosen.
A bowl of fruit is on the table. It contains 6 apples, 5 oranges, and 4 bananas. Brandon
and Connor come home from school and randomly grab one fruit each.
The names of 8 boys and 12 girls from a class are put into a hat. Two names are randomly
chosen.
A card is chosen at random from a standard deck. Without replacing it, a second card is
chosen.
Finding the probability of independent or dependent events:
Marbles in a bag
5 blue, 3 red, 2 yellow
Independent Event
Find P (blue, then a blue) if the marble is replaced.
Dependent Event
Find P (blue, then a blue) if the marble is not
replaced.
P (blue) ∙ P (blue)
P (blue) ∙ P (blue)
5
5
∙
10
10
5
4
∙
10
9
25
100
= 25%
20
90
2
= 229%
Careful: If it is an “or” statement, add the probabilities instead of multiplying them!