Rock, paper, scissors
Two player game
Take turns and record the results
Tally
Player 1
Player 2
Draw
Frequency
Rock, paper, scissors
Continue the table below showing ALL POSSIBLE OUTCOMES
Player 1 Player 2 Result
Stone
Scissors Player 1 WINS
Rock, paper, scissors
Player 1
Rock
Rock
Rock
Scissors
Scissors
Scissors
Paper
Paper
Paper
Player 2
Scissors
Rock
Paper
Scissors
Rock
Paper
Scissors
Rock
Paper
Result
Player 1 WINS
Draw
Player 2 WINS
Draw
Player 2 WINS
Player 1 WINS
Player 2 WINS
Player 1 WINS
Draw
Rock, paper, scissors
PLAYER 2
PLAYER 1
Rock
Rock
Paper
Scissors
R, R
Paper Scissors
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?
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
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….
3 1
 
9 3
Combining two events
Here is another sample space diagram. What is it showing?
Coin 1
Coin 2
HH
HT
TH
TT
Combining two events
Here is another sample space diagram. Complete the table.
Spinner 2
Spinner 1
Red
Blue
Green
1
2
3
Draw the two possible spinners
Yellow
Combining two events
The score from two spinners are added together.
Spinner 2
Spinner 1
1
2
3
4
1
2
3
Complete this sample space diagram
Combining two events
Here are the answers…
Spinner 2
Spinner 1
1
2
3
4
1
2
3
4
5
2
3
4
5
6
3
4
5
6
7
Which scores are most likely to occur?
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.
Combining two events
DICE SCORE 1
2
3
4
5
DICE SCORE 2
1
1
2
3
4
5
6
2
6
6
8
5
6
8
Combining two events
DICE SCORE 2
1
1
2
3
4
5
6
2
3
4
5
6
7
DICE SCORE 1
2
3
4
5
6
3
4
5
6
7
4
5
6
7
8
5
6
7
8
9
6
7
8
9 10
7
8
9 10 11
8
9 10 11 12
Expected frequency
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
1
 300
3
= 100 DRAWS
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)
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
5
P(Train is late) =
1

30 6
Relative frequency
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 :
(a) A student achieves a gold
certificate
(b) A student achieves a pass
(c) Which certificate are
students most likely to achieve
Certificate
Gold
Silver
Bronze
Pass
Frequency
14
49
25
12