1. Solve the following equation in two ways.
Topic: Probability
Aim: How do we find the probability of simple events and what is the difference between theoretical and experimental 
probability?
Do Now:
Solve the following equation in two ways.
Method #1 Method #2
3(x - 2) = 21
3(x - 2) = 21

3. Introduction to Probability:
Lucky you! You won a chance to select a prize from the Grab Bag. Inside the Grab Bag, there are CD's. Here is a list of the artists and their genre:
One Direction (Pop)
Drake (R&B/Hip Hop)
Beyonce (Pop)
Selena Gomez (Pop)
Backstreet Boys (Pop)
Lil Wayne (R&B/Hip Hop)
Pitbull (reggaeton)
Beatles (Rock)
One Republic (Rock)
Bon Jovi (Rock)
If you reach your hand in and pick out a CD, find the 
probability (in simplest form) of picking:
1) a rock CD
2) a pop CD
3) a CD by a group
4) a CD by a single artist

4. Introduction to Probability
An outcome is the result of some activity or experiment.
A sample space is the set of all possible outcomes of a given event.
What is the sample space for rolling a standard fair die?
{1, 2, 3, 4, 5, 6}

5. Introduction to Probability Introduction to Probability
A probability is a chance that an event will happen.  
 Probability written
 as a ratio is  
Probabilities can be written as a fraction, a decimal or    a percent.
__# of favorable outcomes____
P(event) =
total # of possible outcomes

6. Introduction to Probability Introduction to Probability
As the chart below shows, probabilities range from 0 to 1.
If an event is impossible and will never occur, the probability is 0.
If an event is absolutely certain to occur, the probability is 1.
Events that are ___________ have a probability greater than 0.5.
Events that are ___________ have a probability less than 0.5.
Introduction to Probability

7. Probability Line

8. certain to happen, impossible, likely to happen, unlikely to happen
A fair die is rolled, and the outcome noted. Determine whether each
of the following outcomes is:
certain to happen, impossible, likely to happen, unlikely to happen
(a) rolling a 2  ______________________________
(b) rolling a number less than 3 ______________________________
(c) rolling a 7  ___________________________  
(d) rolling a number less than 10____________________________
(e) rolling a number greater than 1 ______________________________
(f) rolling a factor of 6 ______________________________
(g) rolling a multiple of 3 ______________________________
(h) rolling a number that is an integer____________________________
(i) rolling a negative number ______________________________
Example Problems

9. How do you find the probability of an event
not happening?
Let's take a look at an example:
The probability of the complement of an event is
one minus the probability of it occuring .
The probability that Bill will graduate from college is What is the probability that Bill will not graduate from college? Express your answer as a fraction, decimal, and percent.
To find the complement
of an event:
P(NOT E)= 1 - P(E)

10. Introduction to Probability
Theoretical Probability vs
Experimental Probability
Theoretical Probability is based on 
knowing all of the equally likely outcomes of an event.
Given by:
Experimental Probability is an estimate 
based on repeated trials of an 
experiment.
Given by:
# of times an event occurs
total # trials
# of ways an event can occur
total # of possible outcomes

11. #1. Answer the following questions based on a quarter being tossed.
Example Problems
#1. Answer the following questions based on a quarter being 
tossed.
(a) What is the probability that it will land on heads? ________
(b) What kind of probability did you use? _________________
(c) If you toss the coin 32 times, how many times will you 
expect it to land on heads?

12. Example Problems
#2. Toss a fair coin 16 times. Record your results below with 
tallies, then answer the questions that follow based on the chart 
you made.
(a) What is the probability that it will land on heads? ________
(b) What kind of probability did you use? _________________
(c) If you toss the coin 32 times, how many times will you 
expect it to land on heads?
Heads
Tails

13. Practice Problems
#1.) Stephanie has 5 silver bracelets and 2 gold bracelets in her 
jewelry box. Stephanie randomly picks one bracelet. Which statement 
best describes which bracelet she will probably pick?
(1)  She probably will pick a gold bracelet.
(2) She definitely will pick a gold bracelet
(3)  She probably will pick a silver bracelet.
(4)  She definitely will pick a gold bracelet

14. Practice Problems
#2.) A spinner is divided into five equal sections numbered 1 through 5. 
Predict how many times out of 240 spins the spinner is most likely to 
stop on an odd number.
(1)  80
(2) 96
(3) 144
(4) 192

15. Practice Problems Find the probability of landing on a. the number 7
#3.) Use the equally sectioned spinner for the following problems. 
Express each probability as a fraction, a decimal, and a percent.
Find the probability of landing on 
a. the number 7 
b. a multiple of 3 
c. an integer 
d. an irrational number 

16. What is an example of an event with a probability of 1?
Summary
What is probability?
What is an example of an event with a 
probability of 1?
Explain the difference between theoretical 
probability and experimental probability.

17. Homework
Complete Handout
Have a nice weekend !!!