1. 5-8 Probability and Chance

2. Probability
Probability is a measure of how likely it is for an event to happen.

3. The probability of an event is always between 0 and 1, inclusive
The probability of an event is always between 0 and 1, inclusive. If an event cannot happen, its probability is 0. If something is certain to happen, its probability is 1 1 2 1
impossible
50-50 chance
certain 0%
50%
100%

4. Vocabulary Probability- P(event) Outcome Event Sample Space
How likely it is for an event to occur
Outcome
The result of a single trial
Event
Any outcome or group of outcomes in an experiment
Sample Space
All the possible outcomes

5. For instance…
Let’s use the example of rolling a number cube (like dice).
An event could be rolling an even number
What’s the sample space?
1, 2, 3, 4, 5, 6
Which are the favorable outcomes?
2, 4, 6

6. Theoretical Probability
Use this formula when…
all outcomes are equally likely to occur.
P(event) = number of favorable outcomes
number of possible outcomes
P(rolling an even) =
P(rolling a number greater than 2 on a die)

7. 1. What is the probability that the spinner will stop on part A?C D
What is the probability that the spinner will stop on
An even number?
An odd number?
1/3 3 1 2
2/3 A
3. What fraction names the probability that the spinner will stop in the area marked A? C B
1/3

8. Probability Questions
Lawrence is the captain of his track team. The team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue?
3/8
blue
blue
green
black
yellow
blue
black
red

9. -You can express probability as a fraction or a percent:
Example 2: If a bag contains 1 blue cube, 3 red cubes, and 4 yellow cubes what is the probability of selecting a red cube?
-You can express probability as a fraction or a percent:
An impossible event would be 0%
Event equally likely to happen would be 50%
Event certain to happen would be 100%
Example of a certain event: having a test on this stuff.
Example of an impossible event: having it reach 1000 in January.

10. -When finding the probability of two events, this or that, add the two probabilities together.
Example 3: Find the probability of the following events below.
a.) What is the probability of rolling a 6 or a 4 on a dice?
b.) What is the probability of rolling an even number on a dice or rolling a 1?
c.) What is the probability of not rolling a number greater than 3.

11. CHILDREN A family has two children
CHILDREN A family has two children. Draw a tree diagram to show the sample space of the children’s genders. Then determine the probability of the family having two girls.
There are four equally-likely outcomes with one showing two girls.
Answer: The probability of the family having two girls is

12. COINS A game involves flipping two pennies
COINS A game involves flipping two pennies. Draw a tree diagram to show the sample space of the results in terms of heads and tails. Then determine the probability of flipping one head and one tail.
Answer:

13. Sample Space
Definition: Sample Space: the set of all possible outcomes
Sample Space is used to create a chart or table to solve the problem.
When flipping a coin, the sample space is heads or tails.
heads tails

14. Know: Probability = Solve: Each die has 6 sides Practice:
Playing Monopoly or Backgammon, you get to roll again if you roll doubles. What is the probability of rolling doubles?
Know:
# of ways a certain outcome can occur
Probability =
# of possible outcomes
Each die has 6 sides
Solve:
Make a table showing all the combinations that you could roll on a pair of dice as ordered pairs.

15. Second die Fi rs t d ie Sample Space for Rolling two Die 1 2 3 4 5 6 1
Fi rs t
d ie 1 2 3 4
5 6
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

16. Second die Fi rs t d ie Sample Space for Rolling two Die
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Fi rs t
d ie
Second die
Sample Space for Rolling two Die
There are 6 ways to get doubles. There 36 possible outcomes.

17. There are 6 ways to get doubles. There 36 possible outcomes.
# of ways a certain outcome can occur
Probability =
# of possible outcomes

18. There are 6 ways to get doubles. There 36 possible outcomes.
# of ways a certain outcome can occur
Probability =
# of possible outcomes

19. There are 6 ways to get doubles. There 36 possible outcomes.
Probability =
# of possible outcomes

20. There are 6 ways to get doubles. There 36 possible outcomes.
Probability =
# of possible outcomes

21. There are 6 ways to get doubles. There 36 possible outcomes.
Probability = 36

22. There are 6 ways to get doubles. There 36 possible outcomes.
Probability = 36
Question:
What is the probability of rolling doubles?
Simplify 6 36 1 6 = 1 6
The probability of rolling doubles is

23. CHANCE
Chance is how likely it is that something will happen. To state a chance, we use a percent.
Probability 1
Equally likely to happen or not to happen
Certain to happen
Certain not to happen
Chance
50 % 0%
100%

24. Homework
Pg. 249 #6-24 even
Extra Credit #26 – 4 pts. ec