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# Probability

Covering the Junior Cert Probability Chapter
by

## Diarmuid McCarthy

on 1 October 2014

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#### Transcript of Probability

Principles of Counting
Theories of Counting
Definition of Outcomes
Outcomes
There are 5 possible outcomes
Possible outcomes......
What are the possible outcomes in this competition?
You are then in a javelin throwing competition with 4 people altogether in it
You could possibly come 1st, 2nd, 3rd or 4th!
Similar to the other event.....
The consequences of any event/experiment are called the outcomes
Imagine you are running in a race with 5 people in it, what are the possible outcomes?
You could come 1st, 2nd, 3rd, 4th or 5th
Can you think of an example of something that has outcomes??
Simple?
At the end of the sports day you have competed in two events.
List out the possible outcomes for both events....
You could:
1st in race, 1st in Javelin
1st in race, 2nd in Javelin
2nd in race, first in Javelin.....etc.
How many outcomes are there in total?
Multiply the number
of outcomes in each event.....
Event 1: Race - How many outcomes?

Event 2: Javelin - How many outcomes?
Conclusion:
At the end of the day there were
20 possible outcomes between
the race and the javelin
More examples
this way!!
Other events with outcomes:
When you throw a dice......
Possible outcomes?
You could throw a:
1, 2, 3, 4, 5, or a 6
What if you threw a dice, and straight away after you flipped a coin.....?
Event 1:

6 possible outcomes
Event 2:

2 possible outcomes
In total in this event there are
12 possible outcomes!
PAge 41,
Q1 and Q2
Possible outcomes:
10, 11, 12, 13, 14
There are 5 possible outcomes
Event 1: Bag A
3 possible outcomes
Event 2: Bag B
2 possible outcomes
Total possible outcomes
= 6
Event 1:
Main course
3 outcomes
Event 2:
Desert:
2 outcomes
Total possible outcomes:
= 6
Tree Diagram

Spin 1:
Green

Blue
Spin 2
Green

Blue
Green

Blue
Spin 3
Green

Blue

Green

Blue
Green

Blue

Green

Blue
Outcomes
Green, Green, Green
Green, Green, Blue
Blue, Blue, Blue
Blue, Blue, Green
Blue, Green, Green
Green, Blue, Blue
Green, Blue, Green
Blue, Green, Blue
Manchester United and Tottenham are to
play each other in three games during in the
season.
Use a tree diagram to list the possible outcome
over the three games
V
Tree Diagram
Game 1
Man U

Draw

Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Game 2
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U
Draw
Spurs
Man U, Man U, Man U
Man U, Draw, Man U
Man U, Draw, Draw
Man U, Man U, Spurs
Man U, Man U, Draw
Man U, Draw, spurs
Man U, Spurs, Man U
Man U, Spurs, Spurs
Man U, Spurs, Draw
Draw, Man U, Man U
Draw, Man U, Draw
Draw, Man U, Spurs
Spurs, Man U, Spurs
Draw, Draw, Man U,
Draw, Draw, Spurs,
Draw, Draw, Draw
Draw, Spurs, Man U
Draw, Spurs, Draws
Draw, Spurs, Spurs
Spurs, Man U, Draw
Spurs, Man U, Man U
Spurs, Draw, Man U
Spurs, Draw, Draw
Spurs, Draw, Spurs
Spurs, Spurs, Man U
Spurs, Spurs, Spurs
Spurs, Spurs, Draw
Game 3
List of Outcomes
Two way tables
Two spinners are spun one after another. Spinner 1
has number 1-4 on it, while Spinner 2 has numbers
6 - 9 on it

(i) How many outcomes are there?
(ii) How many outcomes add up to 8?
(iii) How many outcomes add up to greater than 7?
How many add up to 8?

How many are greater than 7?
How many of the outcomes are greater than 8?
How many of the outcomes are less than 2?
Which is more likely, odd or even?
What fraction are even?
What % of the scores are odd?
+
+
x
How many ways off the
island are there??
There are 4 places to leave the island
How many ways onto the other
island are there?
There are 6 ways onto the island
6 x 4 = 24
There are 24 possible routes to get
from one island to the other
First digit:
9 options
2nd Digit
8 options
3rd digit
7 options
Total Codes:
9 x 8 x 7
= 504 codes
If you could use the same number each time?
1st digit:
9 choices
2nd digit:
9 choices
3rd digit:
9 choices
9 x 9 x 9
= 729 codes
Ball 1:
42 choices
Ball 5:
38 choices
Ball 3:
40 choices
Ball 2:
41 choices
Ball 4:
39 choices
Ball 6:
37 choices
Total possibilities: 42 x 41 x 40 x 39 x 38 x 37
= 3,776,965,920
What about the
European Lotto???
Euromillions: You need 5 numbers from a pot of 50 balls, AND 2 numbers from a pot of 11.....
So that's:
50 x 49 x 48
x 47 x 46
= 254,251,200
And....
11 x 10
= 110
= 254,251,200 x 110
= 27,967,632,000 possible combinations!!!
Probablity
Probablility
What comes to your mind
when you hear "probablity"
Importance of Maths????
Probability Scale
Impossible
Certain
0
1
Terminology
Trial - An experiment in Probabity

Outcome - The possible results of a trial

Sample Space - The set of all possible ___________outcomes from a trial
For Example..........
A teacher is putting his 6 pupils in groups of two. He puts Michael, Elaine and Martin's names in one bag, and Peter, Megan and Sarah in another bag. He then draws them out randomly.
Use a tree diagram to list out the sample space.

Bag 1
Possible outcomes
A teacher is putting his 6 pupils in groups of two. He puts Michael, Elaine and Martin's names in one bag, and Peter, Megan and Sarah in another bag. He then draws them out randomly.
Use a tree diagram to list out the sample space.
Michael

Elaine

Martin
Peter

Megan

Sarah
Peter

Megan

Sarah
Peter

Megan

Sarah
Bag 2
Possible Outcomes
Sample Space
1. Michael, Peter

2. Michael, Megan

3. Michael, Sarah

4. Elaine, Peter

5. Elaine, Megan

6. Elaine, Sarah

7. Martin, Peter

8. Martin, Megan

9. Martin, Sarah
Sample Space
1. Michael, Peter

2. Michael, Megan

3. Michael, Sarah

4. Elaine, Peter

5. Elaine, Megan

6. Elaine, Sarah

7. Martin, Peter

8. Martin, Megan

9. Martin, Sarah
Questions:
How many possible groups are there altogether?

What is the probability that Michael and Sarah will be picked together first?

What is the probability that the first group picked will be all boys?

What is the probability that the first group picked will be all girls?

What is the probability that the first group picked will be a boy and a girl?
Christmas Exam
Christmas Exam
Q1. Indices, Scientific Notation (old book)
Q2. Simultaneous Eqs and Quadratics (old book)
Q3. Probability (Active Maths)
Q4. Coordinate Geometry (Active Maths)
Q5. Trigonometry (Active Maths)
What is the sample space?
1, 2, 3, 4, 5, 6
(i) 1/6

(ii) 1/6

(iii) 0
(iv) 3 even numbers...
3/6
= 1/2

(v) 2/6
= 1/3

(iii) 1
(certain)
What is the sample space here?
Ace - 10
Jack
Queen
King

13cards
Ace - 10
Jack
Queen
King

13cards
Ace - 10
Jack
Queen
King

13cards
Ace - 10
Jack
Queen
King

13cards
Page 67
How many students are there in the class?
20 students
(i) 7/20

(ii) 4/20

(iii) 11/20

(iv) 3/20

(v) 16/20
Sample Space
1, 3, 6, 8, 9, 77, 89
How many outcomes altogether?

= 7
Full transcript