Lesson 38-1: Probability of a Single
Event
We will understand probability in
real-world situations
and
I will represent sample spaces as
lists and calculate the probability of
a single event.
May 11, 2017
Flip a coin 10 times. Record your results.
Write your results as a ratio and then as a
percent.
Did what you actually flipped match what you
predicted?
Why or why not?
About 30
About 10
About 20
The probability of an outcome is written in symbols as
P(outcome), where the P stands for probability.
For example, the probability that the outcome is an even
number can be written as P(roll results in an even number), or
simply as P(even).
When we roll the cube, as described in Item 1, we expect to
get an even number about half of the time.
Another way of saying this is that, when you roll the cube, the
probability of getting an even number is ½.
To write this using probability notation,
10 1
P(5) 

60 6
20 1
P( 5) 

60 3
A probability experiment is the process of observing
an outcome when the outcome is not known prior to
the experiment.
An outcome is the result of a probability experiment.
The sample space is the set of all possible outcomes.
An event is any outcome or group of outcomes from a
probability experiment.
The probability of an outcome tells you what part of
the time you would expect the outcome to occur.
To generalize, if all the outcomes in the sample space
are equally likely, then the probability of an event is
given by
{1, 2, 3, 4}
1
P(2) 
4
3
P( 2) 
4
P( 4) 
0
0
4
4
P( 0)   1
4
• The probability of an outcome is a number
between 0 and 1, inclusive.
• It can be written as a fraction, a decimal, or
a percent.
• How large the probability is tells us how
likely the event is to occur.
1
P(Casey) 
12
6 1
P(female) 

12 2
0
P(Last name starts with Z) 
0
12
12
P( 30) 
1
12
3 1
P(Last name starts with B) 

12 4
9 3
P(Last name doesn't start with B) 

12 4
Yes. When you add the probability that an event
happens to the probability that the event does not
happen, you are covering all the possibilities, and
therefore the result must be 1.
GBB
BBB
BBG
BGB
BGG
P(3G) 
1
8
3
P(2G) 
8
GBB
BBB
BBG
BGB
BGG
P( 2G) 
4 1

8 2
3 5
P( 2G)  1  
8 8