This document provides an introduction to simple probability concepts including: - Definitions of outcomes, favorable outcomes, and theoretical probability - Examples of calculating probability for single-step experiments like rolling a die - Representing two-step experiments using ordered pairs and calculating probabilities using tables - The relationship between experimental probability from trials and theoretical probability as the number of trials increases

1. SIMPLE PROBABILITY

2. A real life example
Victorian numbers plates usually have 3 letters and 3
numbers. What would happen if they consisted of
only 6 numbers eg 1,2,3,4,5,6?

3. • Learning Intention
- To understand the language of simple
probability
- Success Criteria
- I understand the language of simple
probability

4. Simple Probability
Explicit Vocabulary
-an outcome is a particular result of an experiment
-A favourable outcome is one that we are looking
for
-The theoretical probability of a particular result is
defined as
Pr = number of favourable outcomes
number of possible outcomes
- An ordered pair (a,b) displays the result of a two
step experiment.
- A two way table sets the pairs out logically

5. Worked Example
Tom rolls a fair 6-sided die.
a. What are all the possible results that could be obtained?
b. What is the probability of obtaining : The number 4?
There are 6 outcomes- 1,2,3,4,5,6. These are all the possible results.
THINK Write
1. Write the number of possible outcomes.
4 occurs once. Write the number of number of possible outcomes = 6
possible outcomes.
2. Write the rule for probability p(event) = number of favourable outcomes
Number of possible outcomes
3. Substitute the known values into
the rule and evaluate. P(4) = 1/6
4. Answer the question.
The probability of obtaining a 4 is 1/6

6. - What is the probability of obtaining a number
greater than 2?
THINK Write
1. Write the number of favourable Number of favourable outcomes = 4
and possible outcomes. Number of possible outcomes = 6
Greater than 2 is 3,4,5,6
2. Write the rule for probability
3. Substitute the known values into p(greater than 2) = 4
the rule and evaluate. 6
4. Answer the question. P(greater than 2) = 2/3
The probability of obtaining a number greater
than 2 is 2/3

7. What is the probability of obtaining an odd number?
THINK Write
1. Write the number of favourable Number of favourable outcomes = 3
and possible outcomes. Number of possible outcomes = 6
odd number is 1,3,5
2. Write the rule for probability
3. Substitute the known values into p(Odd number) = 3
the rule and evaluate. 6
4. Answer the question. P(odd number) = 1/2
The probability of an odd number is ½ or 50%

8. Using a table to show sample space
• Some experiments take 2 steps/stages
eg toss 2 coins, or roll a die and toss a coin etc
When we write this outcome it is written as an
ordered pair
Eg pair (H,6) would correspond to getting a head
on the coin and a 6 on the die

9. A worked problem - In table form
a. Draw a table to show the sample space for
tossing a coin and rolling a die.
b. How many outcomes are possible?
c. Determine the probability of obtaining
i) A head
ii) A tail and an even number
iii) A 5
iv) A tail and a number greater than 2

10. Head Tail
1 H1 T1
2 H2 T2
3 H3 T3
4 H4 T4
5 H5 T5
6 H6 T6
A. THE SAMPLE SPACE FOR TOSSING A COIN AND ROLLING A DIE IS:
(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5),(T,6)
B THERE ARE 12 DIFFERENT OUTCOMES
C (I) Getting a head
Favourable outcomes = 6 Possible outcomes = 12
Rule is P(Event) = number of favourable outcomes = 6/12 = 1/2 = 50
number of possible outcomes
P(head) = 50%

11. C (ii) a tail and an even number
Number of favourable outcomes = 3
Number of possible outcomes = 12
P(tail and an even number) = 3/12 = 1/4 = 25%
C(iii) a 5
Number of favourable outcomes = 2
Number of possible outcomes 12
P(5) =2/12 = 1/6
C(iv) a tail and a number greater than 2
Number of favourable outcomes 4
Number of passible outcomes is 12
P(tail and a number greater than 2) = 4/12 = 1/3

12. Experimental Probability versus Actual
Probability
• The more times an experiment is performed
the closer the average of the results will be to
the expected answer
• So the long term trend from a large number of
trials will show that the experimental
probability will match those of the theoretical
probability

13. Let’s try it by tossing a coin 10 times
Draw a tally table in your books like this
Experiment
number
Heads Heads Tails Tails
Tally Count Tally Count
1
2
3
4
5
6
Total Total

14. After the first round:
What is the probability of getting a head?
What is the probability of getting a tail?
How do these values compare with the
theoretical results?
Now toss the coin for another 5 rounds
How does the combined result compare with
the theoretical result?

15. NOW IT’S YOUR TURN
•Log into GenEd and
practice the Simple
Probability questions.
•DON’T FORGET TO SAVE,
SAVE, SAVE!

16. REVIEW
• Write in your books one new thing you have
learnt today.........