Probability Basics
S.CP.A.1
Probability - The chance of an event occurring
 Experiment:
The process of measuring or observing an
activity for the purpose of collecting data.
 Outcome:
A particular result of an experiment.
 Sample Space:
Consists of all the possible outcomes of
the experiment.
 Event: A subset of the sample space that is of
particular interest to the experiment.
For Example:
 Experiment: Rolling a pair of dice
 An outcome: If you rolled a pair of threes, then the
outcome would be 3+3=6
 A sample space: In two standard dice, the smallest
possible outcome would be rolling a pair of ones
(1+1=2) and the largest possible outcome would be
rolling a pair of sixes (6+6=12).
S  2,3,4,5,6,7,8,9,10,11,12
 Event: Rolling a total of two, three, four , or five
given two standard dice
Absolute Certainty
If A represents an event, then P(A) represents the
probability of A occurring.
If an event is certain to occur, then P(A) = 1.
For example: If we let A represent the event
that it is raining today somewhere, then we
can be sure that P(A) = 1
Absolute Impossibility
If an event cannot possibly occur, then P(A) = 0.
For example: If we let B represent the event
that a person can run a mile in one minute,
then we can be sure that P(B) = 0
Some Certainty
Most of the probability questions you will face will
have values between 0 and 1.
number of possible outcomes in which event A occurs
P( A) 
total number of outcomes in the sample space
Probability values may be represented as
decimals, fractions, or percents.
1
success
P( A)  
2 possibilities
Let’s try!!!
 An ordinary penny is tossed once. What is the
probability that it will land on heads?
1
P(heads) 
2

Let’s try!!!
 A penny and a nickel are tossed once. What is the
probability that the penny lands on tails and the
nickel lands on heads?
1
P(tails, heads) 
4
Possibilities: (H,H), (H,T) (T,T) (T,H)

Let’s try!!!
 A penny, a nickel, and a dime are tossed once. What
is the probability that the penny lands on heads and
both the nickel and dime land on tails?
1
P(heads,tails,tails) 
8
Possibilities: (H,H,H), (H,H,T) (H,T,T)
(H,T,H)
(T,T,T)
(T,T,H)
(T,H,H)
(T,H,T)

Let’s try!!!
 A penny, a nickel, and a dime are tossed once. What
is the probability that all coins land on all heads or
they land on all tails?
2 1
P(all heads or all tails )  
8 4

Possibilities: (H,H,H), (H,H,T) (H,T,T)
(H,T,H) (T,T,T) (T,T,H) (T,H,H) (T,H,T)
Dice or Die
 Die – singular
 Dice – plural
 Number cube or die
 Ordinary die = six-sided die
Let’s try!!!
 An ordinary die is rolled once. What is the
probability that it will land on a 2 or 3?
2 1
P(2 or 3) = 
6 3

Let’s try!!!
 An ordinary die is rolled once. What is the
probability that it will land on an odd number?
3 1
P(odd) = 
6 2

Let’s try!!!
 An ordinary die is rolled twice. What is the
probability that each roll will be a 5?
1
P(5,5) =
36

Let’s try!!!
 An ordinary die is rolled twice. What is the
probability that the first roll will land on an even
number and the second roll will land on a number
greater than 4?
6 1
P(even, greater than 4) =

36 6
Let’s try!!!
 An ordinary die is rolled twice. What is the
probability that the sum of the two rolls is 4?
3
1
P(sum of 4) =

36 12

A Deck of Playing Cards
 A deck of ordinary playing cards will include:
4 suits (52 cards)= clubs, diamonds, hearts and spades
1.
2.
3.
4.
2 colors : red (diamonds and hearts), black
(clubs and spades)
4 suits : each suit has aces, 2s, 3s, 4s,…,
10s, jacks, queens, and kings.
Jacks, queens, and kings are called “face”
cards or “picture” cards.
All of other cards are called “non-picture”
cards
Let’s Try!!!
 In drawing one card from a deck of cards, what is the
probability of getting a red jack?
2
1
P(red jack) =

52 26

Let’s Try!!!
 In drawing one card from a deck of cards, what is the
probability of getting any face card?
12 3
P(face card) =

52 13

Let’s Try!!!
 In drawing one card from a deck of cards, what is the
probability of getting any black 4 or black 5?
4
1
P(black 4 or black 5) =

52 13
Let’s Try!!!
 In drawing one card from a deck of cards, what is the
probability of getting any non-picture diamond card?
10 5
P(non - picture diamond) =

52 26