1. Created by Mr Lafferty Maths Dept
Probability
Likelihood Number Line
Combined Probabilities
Relative Frequency
Mutually Excusive Events
Independent Events
18-Nov-18
Created by Mr Lafferty Maths Dept

2. Created by Mr Lafferty Maths Dept
Starter Questions
75o xo
18-Nov-18
Created by Mr Lafferty Maths Dept

3. Created by Mr Lafferty Maths Dept
Probability
Learning Intention
Success Criteria
To understand probability in terms of the number line and calculate simple probabilities.
Understand the probability line.
Calculate simply probabilities.
18-Nov-18
Created by Mr Lafferty Maths Dept

4. Probability Likelihood Line1
0.5
Impossible
Evens
Certain
Not very
likely
Very
likely
Seeing
a butterfly
In July
School
Holidays
Winning the
Lottery
Baby Born
A Boy
Go back
in time
18-Nov-18
Created by Mr Lafferty Maths Dept

5. Probability Likelihood Line1
0.5
Impossible
Evens
Certain
Not very
likely
Very
likely
It will
Snow in winter
Homework
Every week
Everyone getting
100 % in test
Toss a coin
That land
Heads
Going without
Food
for a year.
18-Nov-18
Created by Mr Lafferty Maths Dept

6. Created by Mr Lafferty Maths Dept
Probability
Key Points
To work out a probability
P(A) =
Probability is ALWAYS in the range 0 to 1
18-Nov-18
Created by Mr Lafferty Maths Dept

7. Probability Number Likelihood Line1 2 3 5 4 7 6 8 1
0.5
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Impossible
Evens
Certain 8
P =
Q. What is the chance of picking a number between 1 – 8 ?
= 1 8 4
Q. What is the chance of picking a number that is even ?
P(E) =
= 0.5 8
Q. What is the chance of picking the number 1 ? 1
P(1) =
= 0.125
18-Nov-18
Created by Mr Lafferty Maths Dept 8

8. Probability Likelihood Line
52 cards in a pack of cards 1
0.5
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0.9
Impossible
Evens
Certain
Not very
likely
Very
likely 26
Q. What is the chance of picking a red card ?
P (Red) =
= 0.5 52 13
Q. What is the chance of picking a diamond ?
P (D) =
= 0.25 52 4
Q. What is the chance of picking ace ?
P (Ace) =
= 0.08 52
18-Nov-18
Created by Mr Lafferty Maths Dept

9. Created by Mr Lafferty Maths Dept
Probability
S4 General
Now try Ex 1A & 1B
Ch10 (page 123)
18-Nov-18
Created by Mr Lafferty Maths Dept

10. Created by Mr Lafferty Maths Dept
Starter Questions
37o xo
18-Nov-18
Created by Mr Lafferty Maths Dept

11. Created by Mr Lafferty Maths Dept
Probability
Combined Probabilities
Learning Intention
Success Criteria
To understand combined probability by constructing tables or tree diagrams.
Construct combination tables and tree diagrams.
Calculate probabilities from tables or tree diagrams.
18-Nov-18
Created by Mr Lafferty Maths Dept

12. Probability www.mathsrevision.com Traffic Light 1 Traffic Light 2
Combined Probabilities
On route to school I pass two sets of traffic light.
They work independently.
Complete the table of all possible combinations
Traffic light 2
Calculate Probability :
Both green R A G r
(r,R)
(r,A)
(r,G)
Traffic
Light 1 a
(a,R)
(a,A)
(a,G)
2. At least one green g
(g,R)
(g,A)
(g,G)
3. One is amber one red
18-Nov-18
Created by Mr Lafferty Maths Dept

13. Probability www.mathsrevision.com Traffic Light 1 Traffic Light 2
Combined Probabilities
Another way of representing the data !
Tree Diagram R
(r,R)
Calculate Probability :
Both green
T L2 A
(r,A) r G
(r,G) R
(a,R) a A
T L 1
(a,A)
2. At least one green
T L2 G
(a,G) g
3. One is amber one red R
(g,R) A
(g,A)
T L2
(g,G) G
18-Nov-18
Created by Mr Lafferty Maths Dept

14. Created by Mr Lafferty Maths Dept
Probability
Combined Probabilities
Key Points
List all combinations
(using a suitable table or tree diagram)
2. Interpret information to calculate probabilities.
18-Nov-18
Created by Mr Lafferty Maths Dept

15. Created by Mr Lafferty Maths Dept
Probability
Combined Probabilities
S4 General
Now try Exercise 2
Ch10 (page 124)
18-Nov-18
Created by Mr Lafferty Maths Dept

16. Created by Mr Lafferty Maths Dept
Starter Questions
120o xo
18-Nov-18
Created by Mr Lafferty Maths Dept

17. Created by Mr Lafferty Maths Dept
Probability
Relative Frequency
Learning Intention
Success Criteria
To understand the term relative frequency.
Know the term relative frequency.
Calculate relative frequency from data given.
18-Nov-18
Created by Mr Lafferty Maths Dept

18. Created by Mr Lafferty Maths Dept
Probability
Relative Frequency
Relative Frequency : How often an event happens
compared to the total number
of events.
Example
Daniel
Frances
Number of heads 24 55
Number of tosses 60
100
Joe has a R.F. of heads =
18-Nov-18
Created by Mr Lafferty Maths Dept

19. Created by Mr Lafferty Maths Dept
Probability
Relative Frequency
Relative Frequency : How often an event happens
compared to the total number
of events.
Example
Daniel
Frances
Number of heads 24 55
Number of tosses 60
100
Frances has a R.F. of heads =
18-Nov-18
Created by Mr Lafferty Maths Dept

20. Probability www.mathsrevision.com Joe has a R.F. of heads =
Relative Frequency
Joe has a R.F. of heads =
Frances has a R.F. of heads
Whose relative frequency is closer to P(H) ?
P(H) = 0.5
France’s R.F. is closer to P(H)
Note : The larger the random sample, the closer
the relative frequency is to the probability of the event
18-Nov-18
Created by Mr Lafferty Maths Dept

21. Created by Mr Lafferty Maths Dept
Probability
Relative Frequency
S4 General
Now try Exercise 3
Ch10 (page 126)
18-Nov-18
Created by Mr Lafferty Maths Dept

22. Created by Mr Lafferty Maths Dept
Starter Questions
55o xo
47o
18-Nov-18
Created by Mr Lafferty Maths Dept

23. Created by Mr Lafferty Maths Dept
Probability
Mutually Exclusive
Learning Intention
Success Criteria
To understand that the term mutually exclusive. Understand that we simply add probabilities with this property.
Understand the term
mutually exclusive.
Calculate probabilities for events that have this property.
18-Nov-18
Created by Mr Lafferty Maths Dept

24. Probability www.mathsrevision.com P(A or B) = P(A) + P(B)
Cannot happen at the same time
Probability
Mutually Exclusive
When two events are MUTUALLY EXCLUSIVE
we can simply add their individual probabilities
P(A or B) = P(A) + P(B)
“or”
means add
18-Nov-18
Created by Mr Lafferty Maths Dept

25. Created by Mr Lafferty Maths Dept
Probability
Mutually Exclusive
Example : There are 12 balls in a box.
Q. What is the probability of picking a green ball.
P(G) =
Q. What is the probability of picking a white ball.
P(W) =
Q. What is the probability of picking a green OR white ball.
P(G or W) = P(G) + P(W)
18-Nov-18
Created by Mr Lafferty Maths Dept

26. Created by Mr Lafferty Maths Dept
Probability
Mutually Exclusive
S4 General
Now try Ex 4A & 4B
Ch10 (page 127)
18-Nov-18
Created by Mr Lafferty Maths Dept

27. Created by Mr Lafferty Maths Dept
Starter Questions xo
270o
18-Nov-18
Created by Mr Lafferty Maths Dept

28. Created by Mr Lafferty Maths Dept
Probability
Independent Events
Learning Intention
Success Criteria
To understand that if two events are independent we can simply multiply probabilities.
Understand when two events are independent.
Calculate probabilities for events that are independent.
18-Nov-18
Created by Mr Lafferty Maths Dept

29. Probability www.mathsrevision.com P(R,R) = P(R) x P(R) Spinner 1
Independent Events
Calculate P(R)
for spinner 1
Write down all the possible outcomes
when the two spinners are spun together.
Spinner 2
Calculate (R)
for spinner 2 Y G R Y
(Y,Y)
(Y,G)
(Y,R)
Spinner 1 G
(G,Y)
(G,G)
(G,R) R
(R,Y)
(R,G)
(R,R)
Notice from table P (R,R)
P(R,R) = P(R) x P(R)
18-Nov-18
Created by Mr Lafferty Maths Dept

30. Probability Key Points www.mathsrevision.com P(A and B) = P(A) x P(B)
Independent Events
Key Points
For two independent events A and B we can
multiply the individual probabilities
P(A and B) = P(A) x P(B)
“and” means
multiply
Independent Events
List all combinations.
Calculate individual probabilities.
Multiply them together.
18-Nov-18
Created by Mr Lafferty Maths Dept

31. Created by Mr Lafferty Maths Dept
Probability
Independent Events
S4 General
Now try Exercise 5
Ch10 (page 129)
18-Nov-18
Created by Mr Lafferty Maths Dept