1. 3:4
1/7
2:2
£720
20%
45%
2:3
2/3
3:1

2. Probability Week 06: State how likely or unlikely an event is
Use a probability scale to describe the likelihood of an event
Express probability using fractions, decimals, percentages and words
Describe and analyse outcomes using tables and frequency trees
Use randomness, fairness and likelihood to calculate expected outcomes of experiments
Relate expected outcomes to theoretical probability using the probability scale
Understand why the sum of probabilities equals 1

3. What did we do last week?

4. Probability
Probability is how likely something is to happen An impossible event has probability 0 A certain event has probability 1 A probability experiment is called a trial (rolling a dice once) An event is a particular outcome (rolling a 1 on a dice) Probability can be written as a fraction, decimal, percentage or using words

5. Probability
Probability of an event = number of outcomes in event / total number of outcomes. Probability of rolling a 1 on a dice = how many 1’s / how many numbers in total (1 / 6) The sum of all possible outcomes is 1 Decimal probabilities can be added together Probability of an event not happening is 1 – Probability of an event happening

6. Probability Scale
Probability is given as a value between 0 and 1, with 0 being impossible and 1 being certain:
Impossible
Unlikely
Evens
Likely
Certain
Using the probability scale, what is the probability of:
1. Buying a lottery ticket and winning the jackpot
2. Spinning a coin and getting tails
3. Christmas Day being December 25th
4. Seeing a person with two noses
5. Going on holiday to Mars next year
6. Rain in February

7. Event Probability What is the chance of getting a 6 with one dice?
The probability of an event happening is:
The number of ways that event can happen
The total number of possible outcomes
What is the chance of getting a 6 with one dice?

8. What is the chance of getting a 6 on this spinner?2 4 6 6 2

9. What is the chance of getting an odd number on this spinner?1 2 3 4 5

10. What are the chances of getting a 6 on this spinner?5 4 3 3 6

11. What is the chance of picking a blue counter out of the bag?

12. What is the chance of picking a purple counter out of the bag?

13. Imagine you have a pack of cards
Imagine you have a pack of cards. Using fractions, what is the probability of:
Choosing a red card?
Choosing a King?
Choosing a Diamond card?
Choosing a picture card?
Choosing any numbered card?
Choosing any red picture card?
Choosing any black number card?

17. List all the different combinations from this menu.
The menu in a restaurant has two choices of starter, three choices of main course and two choices of dessert.
List all the different combinations from this menu.
Greg always chooses his three courses at random.
b) What is the probability that he chooses Melon, Chicken pie and Gateau?
Starters
Melon (A)
Pineapple (B)
Main course
Steak (C)
Cod fillet (D)
Chicken Pie (E)
Dessert
Ice Cream (F)
Gateau (G)

18. Forty people take a driving test on Wednesday:
Pass
Fail
Male 10 13
Female 6 11
A person is chosen at random. What is the probability that the person is male?
A person is chosen at random. What is the probability that the person passed the test?

20. 50 times.

21. Relative Frequency
Relative frequency estimates probability when outcomes are not equally likely Relative frequency = number of trials where event occurred / total trials Relative frequency is more reliable when more trials are performed Sample space is a list of all possible outcomes (H or T for one coin)

22. What is the probability that the next car to pass his house will be:
Fred records the colour of 100 cars that pass his house. His results are shown below.
Calculate the relative frequency/experimental probability of each colour.
What is the probability that the next car to pass his house will be:
Red?
Blue?
Not black?
On an average day, 3500 cars pass Fred’s house. Based on his results, how many of these 3500 would we expect to be silver?
Colour
Red
Blue
Silver
Black
Other
Frequency 10 15 38 32 5
Relative Frequency
0.1
0.15
0.38
0.32
0.05
Colour
Red
Blue
Silver
Black
Other
Frequency 10 15 38 32 5
P(red) = 0.1
P(blue) = 0.15
P(not black) = 1 – 0.32 = 0.68
0.38 x 3500 = 1330 cars would be expected to be silver

23. Proportion
There are 30 children in a class in the ratio 2:1. There are 20 boys. What proportion are boys?
With words:
As a fraction:
20 out of 30 20 30
As a decimal:
As a percentage:
66%

24. Direct Proportion
We can use the ratio of something to multiply or divide a quantity as required, e.g:
3 tins of blue paint : one tin of white
If you need to mix 9 tins of blue paint you will need 3 of white

25. Exam Question Year 10 and Year 11 students are in assembly:
Year boys : girls Student data
: boys
: students
Work out the total number of girls in the assembly.

26. Rewrite this recipe to make :
6 cakes b) 18 cakes c) 20 cakes