2.3
Probability and Odds
Objective: Given a description an event, find
the probability and/or the odds of the event
happening (including replacement and nonreplacement).
Probability
P = Probability
S = Success
T = Total
S
P
T
Probability
Probability is a fraction that must be between 0 and 1.
Probability can be exactly 0 or exactly 1.
For example if you are asked P(7) when rolling a standard six sided the answer
0
is but you can just say 0.
6
You can never roll a 7 on a standard six sided die.
For example if you are asked P(number <7) when rolling a standard six sided
die the answer is 6  1 , therefore you can just answer 1.
6 1
You will always roll a number less than 7 on a standard six sided die.
Odds (For)
O = Odds
S = Success
F = Failure
S
OF 
F
Odds (Against)
O = Odds
S = Success
F = Failure
F
OA 
S
Probability and Odds
S
P
T
S
OF 
F
What is the relationship between S, F, and T
in the probability and odds formulas?
S+F=T
Odds
Odds must always stay a fraction or ratio. It can never be reduced to an integer.
4
2
For example if the odds came out to be , you would reduce it to , but you
2
1
would not change it an integer.
Flip A Coin
4 Possible Outcomes
H
H
Flip a
Coin
Twice
T
H
T
T
1 1
1
P(H, H)  
2 2
4
HH
HT
TH
TT
Flip A Coin
8 Possible Outcomes
H
H
Flip a
coin
three times
T
H
T
P(H, H, H)
T
1
1 1 1
  
2 2 2
8
H
T
H
T
H
T
H
T
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Replacement vs.
Non-Replacement
You are reaching into a bag of marbles to
get a marble. There are 3 green, 5 blue,
and 2 red marbles in the bag. What is the
probability that you get a green marble?
Let’s assume you get a green marble and
keep it in your hand. You then reach in
again. What is the probability that the next
marble is also green?
Now what is the probability of those two
things happening together?
7 8
6 7
9 10 11 12
8 9 10 11
5 6
7
8
9 10
4 5
3 4
2 3
6
5
4
7
6
5
8
7
6
9
8
7
Assignment
2.3 Worksheet
Entry Task
• Get a Purple/Blue Book
• Get out pencil and paper
• Find the
a) probability and b) odds of the following events:
1)Rolling a 5 or 6 on a standard die
2)Drawing a red queen from a deck of cards
3)Rolling an odd number on a standard die
4)Drawing a Black Jack, Black Queen, or Black King
5)Rolling a multiple of 5 on a 30 sided die