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Math Tech IIII, Mar 22
Probability I – Introduction and the
Mathematics of Probability
Book Sections: 3.1
Essential Questions: How can I compute the probability of any event?
What is probability and what is the mathematical basis of
computing it?
Standards: PS.SPCR.2, PS.SPCR.7
Probability
What is probability?
• A measure of the likelihood that an event will
happen.
Simple Probability
Terms to Know and Understand
• Outcome – The result of a random phenomenon
• Random –outcomes that occur by chance, and
every outcome has the same chance or is equally
likely
• Event – A collection of outcomes
• Probability – The likelihood that an event will
happen
• Sample Space – A list of all possible outcomes
of a random event
Notation
• The probability of an event will be
abbreviated as follows:
P(event) =
Examples
In a coin flip there are two possible outcomes,
head and tail
The probability of the outcome head of the event
would be expressed as: P(head)
The probability of the outcome tail of the event
would be expressed as: P(tail)
Examples
What is the sample space of the following events?
A) Rolling a die.
B) Flipping a coin.
C) Selecting a marble from a bag containing 3 red, 2 mauve, and
5 clear marbles.
The Mathematical Basis of Probability
• You compute probability, no matter how it
is expressed, by using a ratio.
• A ratio is comparing two numbers by
division.
The most common manifestation of a ratio is a
fraction.
Ratio
• A ratio is a comparison of two numbers by
division
• There are three ways of writing a ratio:
5
5 to 22, or 5:22, or
22
Examples
1) 15 cats to 50 dogs
2) 27 nurses to 9 doctors
3) 8 completions:12 passes
4) 21 hired out of 105 applicants
5) 2 teams : 22 players
6) 7 first downs to 28 first downs
Examples Solutions
1) 15 cats to 50 dogs
3
10
3) 8 completions:12 passes
2
3
5) 2 teams : 22 players
1
2
2) 27 nurses to 9 doctors
3
1
4) 21 hired out of 105 applicants
1
5
6) 7 first downs to 28 first downs
1
4
The Mathematical Definition of Probability
Number of favorable outcomes
P(event) =
Total number of outcomes
In words: The probability of an event is the
ratio of favorable outcomes to the number
of possible outcomes. That number will
always be between 0 and 1.
Expressing Probability
• Probability can be expressed as:
A fraction (in simplest form)
A decimal
A percent (%)
• Probability ranges between 0 and 1 (0% - 100%)
Probability of 0 means the event is impossible
Probability of 1 means the event is a sure thing
The Range of Probabilities
likely
Examples
Which values cannot be the probability of some event?
A) 0.23
F) 1
B) 1.1
G) 3
4
H) 86%
C) 0
3
D)
2
5
E)
9
I) -.15
1
J) 
2
Examples Solutions and Why
Which values cannot be the probability of some event?
A) 0.23
F) 1
B) 1.1 Can’t be more than G) 3
4
one.
C) 0
H) 86%
Can’t be more than
3
D)
I) -.15 Can’t be negative.
one.
2
5
E)
9
1
J) 
2
Can’t be negative.
Examples
The following events occur.
A) A die is rolled.
B) A coin is flipped.
C) A marble is chosen from a bag containing 3 red, 2 mauve, and
5 clear marbles.
In A, what is the probability of rolling a 2?
In B, what is the probability of getting a head?
In C, what is the probability of selecting mauve?
Examples Solutions
The following events occur.
A) A die is rolled.
B) A coin is flipped.
C) A marble is chosen from a bag containing 3 red, 2 mauve, and
5 clear marbles.
In A, what is the probability of rolling a 2?
1
6
In B, what is the probability of getting a head?
In C, what is the probability of selecting mauve?
1
12
5
Probability in this Course
• We will compute simple and multiple event
probability in this class. You will need to
know how to: Create and simplify
fractions, add fractions, subtract fractions,
and multiply fractions over the course of
this unit.
• The calculator can do all of these,
understand how and know the calculator
limitations!
You are a Fraction Expert
• By using MATH then ENTER ENTER
on the calculator, you get a fraction in
simplest form for any calculator fraction
operation.
• A fraction is entered on the calculator as a
division of two numbers (÷)
• You use the same operation to convert a
decimal to a fraction.
Examples
4
7
1
5
3
10
2
9
2
13
1
52
x
+
Convert fractions to decimals and decimals to fractions
4
5
7
30
0.48
0.375
Examples
4
7
1
5
3
10
2
9
2
13
1
52
x
+
Convert fractions to decimals and decimals to fractions
4
5
7
30
0.48
0.375
Class work: Classwork 3/22/17, 1-30
Homework: None