1. How many words can you find relating to probability?
Starter
How many words can you find relating to probability?
1 – 4 = Good
5 – 8 = Ace 9 – 12 = Awesome
13 + = Superstar!

2. Impossible
Could
Likely
Poor
Even
Would
More
Definite
Probable
Good
Unlikely
May
Chance
Won’t
Never
Certain
Possible
Might
Improbable
Less

3. Match the labels to the correct place on the probability scale
likely
unlikely
certain
impossible
even chance
100% chance
no chance
75% chance
50% chance
25% chance

4. Use the words to describe the probabilities of the events below:
You will celebrate your 10th birthday tomorrow.
Tomorrow you will have a cold.
It will rain tomorrow.
You will be struck by lightning tomorrow.
You will have something to drink tomorrow.
Sometime tomorrow you will watch television.
The next person you pass in the corridor will be male.
The sun will rise tomorrow morning.
Rolling the number six on a dice on one throw.
You will still be alive when you are 100.
Impossible ?
Likely
Unlikely
Certain
Even chance

5. To be more accurate, we express probability as a number
Sometimes words aren’t enough!
We’re mathematicians! How can we be more accurate when talking about probability?
To be more accurate, we express probability as a number

6. The probability that an event will happen is a number between 0 and 1
The probability for an event which is CERTAIN = 1
The probability for an event which is IMPOSSIBLE = 0 1 5
0.2
20%
Probability can be expressed as a fraction, a decimal or a percentage

7. Example 1 1 2
or 0.5
If I had a bag containing an apple and a pear, what is the probability that I will pick out the pear? or
50%

8. Example 2
A box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. Work out the probability that the bag of crisps will be: a) salt and vinegar b) cheese and onion c) beef
3/9
4/9
2/9

10. Number of ways of achieving success Number of possible outcomes
Answers
Event
Number of ways of achieving success
Number of possible outcomes
Probability
Throwing a 2 1 6
1 6
Throwing a 5
Throwing an odd number 3
3 6
Throwing more than 3  3
  3 6
Throwing less than 5  4
  4 6
Throwing 2 or more  5
  5 6
Throwing a 7  0
  0 6 = 0
Throwing an even number
Throwing less than 7  6
  6 6 = 1

11. It is impossible that Ethan will take a red sweet from…
Bag 4
Bag 2
Bag 5
Bag 1

12. It is unlikely that Ethan will take a red sweet from…
Bag 4
Bag 2
Bag 5
Bag 1

13. It is even chance that Ethan will take a red sweet from…
Bag 4
Bag 2
Bag 5
Bag 1

14. What is the probability of choosing a red counter from this bag?
7/5
4/12
7/12
1/11

15. What is the probability of choosing a yellow counter from this bag?
7/5
4/12
1/12

16. What is the probability of choosing a green counter from this bag?
7/5
4/12
1/12

17. What is the probability of this spinner landing on pink?
1/12
1/6
2/6

18. What is the probability of this spinner landing on yellow?
2/6
1/3
2/4
1/6

19. What is the probability of this spinner landing on light blue?1
2/6
3/12
3/6

20. What is the probability of this spinner NOT landing on pink?
3/6
5/6
1/6

21. What is the probability of choosing the letter A at random from the word
2/12
3/11
2/11
2/9
MATHEMATICS

22. What is the probability of choosing a vowel at random from the word
3/11
3/10
4/7
4/11
MATHEMATICS

23. What is the probability of choosing a consonant at random from the word
4/11
7/11
7/4
4/7
MATHEMATICS

24. Mutually Exclusive Events
What does mutually exclusive mean?
Mutually exclusive means “can’t happen at the same time”
So, mutually exclusive events are events that cannot happen at the same time
Ask pupils for their own example of a mutually exclusive event
Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards

25. Turning left or turning right
For example
Turning left or turning right
Going to Liverpool at 9am tomorrow, or going to Manchester at 9am tomorrow
(You cannot turn left and right at the same time, or be in two places at once!)

26. What is not Mutually Exclusive
Turning left and scratching your head can happen at the same time
Kings and Hearts, because you can have a King of Hearts

27. The following statements are mutually exclusive…
True or false?

28. True Question 1 Winning a football match AND
Losing the same football match
True

29. False Question 2 Having pizza for dinner AND
Having ice cream for pudding
False

30. Question 3
Getting the bus
AND
Missing the bus
True

31. Question 4
Watching a comedy DVD
AND
Watching a romance DVD
False

32. Question 5
Being awake
AND
Being asleep
True

33. Rolling a number less than 3
Question 6
Rolling a 2 on a dice
AND
Rolling a number less than 3
False

34. True Question 7 A traffic light being red AND
A traffic light being green
True

35. The same baby being a girl
Question 8
A baby being a boy
AND
The same baby being a girl
True

36. Randomly picking a dog from the pound
Question 9
Randomly picking a dog from the pound
AND
The dog being brown
False

37. False Question 10 Me not winning the lottery AND
My friend not winning the lottery
False

38. Probability Bingo Aim: Full House Grid: 9 Grid
Play: Calculate probability
& cross it off

39. Numbers to Use ¼ 0.42 5/6 12% 0.35 ½ 7/15 0.62 30% 13/20 0.4 57%
¼ /6 12%
½ /
30% / %
¾ / %

40. Probability of scoring less than 6 on a normal dice

41. The probability that I will set homework is 0. 66
The probability that I will set homework is What is the probability I will not set homework?

42. The chance of picking a girl from a group of 3 girls and 7 boys.

43. There are 4 white beads, 2 red beads, 1 green bead and 8 blue beads
What is the probability that the bead I pick is NOT blue?

44. The chance of getting 2 heads when 2 coins are flipped.

45. The probability that I choose a girl to answer a question is 0
The probability that I choose a girl to answer a question is 0.58 what is the probability I choose a boy?

46. Tonight I can go to the cinema, visit a friend or stay at home.
I am equally likely to do each thing
What is the probability I stay at home?

47. What is the probability of getting a prime number when a normal dice is thrown?

48. I have red, green and black socks
The probability I wear red socks is 0.15
The probability I wear green socks is 0.23
I am going to wear socks. What is the probability I wear black socks?

49. At a running club 25% of the runners have run a marathon.
What is the probability a runner picked at random has not run a marathon?

50. A box of chocolates has 5 strawberry creams, 4 coffee creams, 9 caramels and 2 toffee dreams.
What is the probability that I pick a coffee cream or a caramel?

51. In an experiment a drawing pin lands point down 9 times out of 20.
What is the experimental probability that the pin will land point up?

52. The probability that it rains tomorrow is 0. 43
The probability that it rains tomorrow is What is the probability that it will NOT rain?

53. In a year group of 200 students 70 are left handed
In a year group of 200 students 70 are left handed. What is the probability that a randomly picked student will be left handed?

54. In a group of 50 teachers 6 are mathematicians.
What is the probability that a teacher picked at random will be a mathematician?

55. I observe 100 cars. I see 40 red cars
I observe 100 cars. I see 40 red cars. Use relative frequency to estimate the probability that the next car I see will be red.

56. What does exhaustive mean?
Exhaustive Events
What does exhaustive mean?
The probabilities of all possible outcomes add up to 1.
Ask pupils for their own example of a mutually exclusive event
Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards

57. =1 Example 1 The probability of getting a 1 is 1 6
Total: =1

58. Example 2
A box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. What is the probability they are beef?
Flavour of crisp
Salt & Vinegar
Cheese & onion
Beef
Probability
3 9
4 9
1 – ( )
= 2 9

59. Example 3 P(bus) = 1 – (0.36 + 0.52 + 0.06) = 0.06
In a survey during walk to school week, all the pupils at Winsford Academy either cycle, walk, come by bus or still come in a car. The probabilities they travel each way are below. What’s the probability they come by bus?
Method of Travel
Cycle
Walk
Bus
Car
Probability
0.36
0.52
0.06
P(bus) = 1 – ( )
= 0.06

61. Answers – Q1 & 2 Event M or N? E?
Tossing a head with a coin / Tossing a tail with a coin M
E (H or T)
Throwing a number less than 3 with a dice / Throwing a number greater than 3 with a dice
Drawing a Spade from a pack of cards / drawing an Ace from a pack of cards N
Drawing a Spade from a pack of cards / Drawing a red card from a pack of cards
(Choosing from a group of three girls and two boys): Choosing two girls / choosing two boys
Drawing a red card from a pack of cards / drawing a black card from a pack of cards E
Winning a football match / Drawing a football match
Eating toast for breakfast / Eating chips for dinner

62. Answers – Q3, 4, 5 & 6 Question 3 P (not h) = 0.7 P (not h) = 0.48
0.24
Question 5
P (purple) = 0.1
P (purple) = 0.2
P (purple) = 4%
P (purple) = 7/20
Question 6
P (3) = 3/8
P (red) = 1/8
i) M ii) N iii) M iv) M

64. Which horse is most likely to win? Why?
Are there any horses that definitely won’t win?
How do you know?

65. Which horse do you think will win? Play now with the person next to you.

66. + 7 2 3 4 5 6 7
From this sample space diagram we can see that there are 36 possible outcomes when two dice are thrown. 7 3 4 5 6 7 8 4 5 6 7 7 8 9 7 5 6 7 8 9 10
Six of these have a total of 7. 7 6 7 8 9 10 11 6
P(7) = 7 36 7 8 9 10 11 12

67. I am choosing an outfit…
How many different combinations could I have?
What is the probability of choosing a red t-shirt?

68. So the probability of choosing a red t-shirt =
Putting it in to a sample space diagram makes it a lot easier to calculate the probability
Trousers
Blue
Black
Grey
Orange
T-Shirt
Red
White 4 16
So the probability of choosing a red t-shirt =

69. Now on whiteboards… Trousers Blue Black Grey Orange T-Shirt Red White
Trousers
Blue
Black
Grey
Orange
T-Shirt
Red
White
As a fraction work out the probability of: (a) Choosing a white t-shirt with either blue or grey trousers (b) Not choosing orange or blue trousers 1 8 1 2

70. Answers Question 1 1/12 Question 2 3/16 2/16 4/16 Question 3 15/25
Question 2
3/16
2/16
4/16
Question 3
15/25
3/25
12/25
7/25
4/25
Question 4
8/36
4/36
24/36
Question 5
2/24
6/24
7/24
1/24
5/24

71. True False True False True False Starter – True or False
You are equally likely to get a heads or tails when flipping a fair coin
True
False
You are more likely to get an even number when rolling a fair die
The probability of picking a red card is 2/3
True
The probability of landing on a 1 on the spinner is 1/4 2 5 4 3
False
The probability of not picking a black card is 4/6
True
The probability of choosing an ‘A’ from is 2/10
False

72. Ends of first and second level branches show the different outcomes.
Probability Trees
The probabilities for each event are shown along the arm of each branch and they sum to 1.
Ends of first and second level branches show the different outcomes.

73. Rebecca has nine coloured beads in a bag
Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead.
Draw a tree diagram showing all possible outcomes.
Calculate the probability that Rebecca chooses:
(i) 2 green beads (ii) A black followed by a green bead.
First Choice
Second Choice
black
black
green
black
green
green

74. Peter has ten coloured cubes in a bag
Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random.
Draw a tree diagram showing all possible outcomes.
Calculate the probability that Peter chooses:
(i) 2 red cubes (ii) A blue cube followed by a red cube.
First Choice
Second Choice
red
red
blue
red
blue
blue

75. The ‘And’ and ‘Or’ Rules
Calculate the probability of picking one milk chocolate and one dark chocolate in any order.
First Pick
Second Pick
Milk
Milk
Milk AND dark OR dark AND milk
= x x
= 432
870
Dark
Milk
Dark
Dark

77. Extension
There are 4 blackcurrant sweets, 3 apple sweets and 4 strawberry sweets in a bowl.
I pick two sweets (one after the other).
What is the probability that I pick two sweets of the same flavour?

78. Answers 24 49 42

79. Pair Activity
You are running a stall at a carnival using the pack of cards, any heart wins.
At £10 a go, what would you make prize y in order to make a profit, and to make the game enticing?
First Card
Second Card £y
Not £3
£10 £3
Not
Not £0

80. Plenary
Summarise in a text message (160 characters) what the key learning points are from today’s lesson.