2. Rock, paper, scissors Tally Frequency Player 1 Player 2 Draw
Two player game
Take turns and record the results
Tally
Frequency
Player 1
Player 2
Draw

3. Rock, paper, scissors Player 1 Player 2 Result Stone Scissors
Continue the table below showing ALL POSSIBLE OUTCOMES
Player 1
Player 2
Result
Stone
Scissors
Player 1 WINS

4. Rock, paper, scissors Player 1 Player 2 Result Rock Scissors
Player 1 WINS
Draw
Paper
Player 2 WINS

5. Rock, paper, scissors
PLAYER 1
Rock
Paper
Scissors
R, R
PLAYER 2

6. Rock, paper, scissors Answer these questions in your books
Who is more likely to win?
Explain why this is a fair game to play.
After 60 games, how many games should be a draw?
Why are the frequencies not all the same?
How can you even up the results for each player?

7. Rock, paper, scissors Who is more likely to win? Noone
Explain why this is a fair game to play.
As all possible outcomes are equally likely
After 60 games, how many games should be a draw?
Theoretically, 20.
Why are the frequencies not all the same?
Because this is just an experiment
How can you even up the results for each player?
You should play many more games

8. Rock, paper, scissors Calculating chance
PROBABILITY = a measured chance of something happening.
PROBABILITY = Favourable outcomes
TOTAL number of outcomes
Eg. The probability of winning at Rock, Paper, scissors is….

9. Combining two events Coin 1 Coin 2 HH HT TH TT
Here is another sample space diagram. What is it showing?
Coin 1
Coin 2 HH HT TH TT

10. Combining two events Spinner 1 Spinner 2
Here is another sample space diagram. Complete the table.
Spinner 1
Red
Blue
Green
Yellow 1 2 3
Spinner 2
Draw the two possible spinners

11. Combining two events Spinner 1 Spinner 2
The score from two spinners are added together.
Spinner 1 1 2 3 4
Spinner 2
Complete this sample space diagram

12. Combining two events Spinner 1 Spinner 2
Here are the answers…
Spinner 1 1 2 3 4 5 6 7
Spinner 2
Which scores are most likely to occur?

13. Combining two events Two normal dice are rolled at the same time.
Design a sample space diagram that can record the sum of the scores of the two dice.

14. Combining two events
DICE SCORE 1 1 2 3 4 5 6 8
DICE SCORE 2

15. Combining two events DICE SCORE 1 1 2 3 4 5 6 7 8 9 10 11 12

16. Expected frequency = 100 DRAWS
Expected frequency = probability x number of trials
You can use the probability of an event to predict the number of times an outcome might happen.
Example : Two people play the game Rock, Paper, Scissors, 300 times. Estimate the number of draws there will be.
Out of 300 games, we would EXPECT
= 100 DRAWS

17. Questions Expected frequency = probability x number of trials
1. A dice is rolled 90 times. How many sixes would you expect?
2. A coin is flipped 80 times. How many heads would you expect?
3. Two out of three people prefer Summer than winter holidays.
Out of 1000 people asked, how many prefer Summer holidays?
4. 1 out of every 8 people in England are vegetarian. How many vegetarians are there in england (Pop. England = 64 million)

18. Relative frequency Relative frequency = estimated probability
You can ESTIMATE probability using an experiment or historical information
Example : A train is late 5 times in April. Estimate the probability that it will be late on the first day of May.
Out of 30 days, 5 days the train was late. So
P(Train is late) =

19. Relative frequency Certificate Frequency Gold 14 Silver 49 Bronze 25
Relative frequency = frequency of event
total frequency
A table shows the levels achieved by 100 students in a maths challenge competition .
Estimate the probability that :
Certificate
Frequency
Gold 14
Silver 49
Bronze 25
Pass 12
(a) A student achieves a gold certificate
(b) A student achieves a pass
(c) Which certificate are students most likely to achieve