1. Rock, Paper, Scissors
A Probability Experiment

2. The language of probability
Probability is a measurement of the chance or likelihood of an event happening.
Words that we might use to describe probabilities include:
50-50 chance
likely
unlikely
poor chance
certain
very likely
possible
Ask pupils to give examples of sentences for each phrase.
impossible
even chance
probable

3. Rock, paper, scissors
In the game rock, paper, scissors two players have to show either rock, paper or scissors using their hands as follows:
rock
paper
scissors
The rules of the game are that:
Scissors beats paper (it cuts).
Paper beats rock (it wraps).
Rock beats scissors (it breaks).
If both players show the same hands it is a draw.

4. Rock, paper, scissors
What is the probability that both players will show the same hands in a game of rock, paper, scissors?
We can list all the possible outcomes in a two-way table using R for Rock, P for Paper and S for Scissors.
Scissors
Paper
Rock
First player
Second player SS SS SP SR PS PP PP PR RS RP RR RR 3 9 = 1 3
P(same hands) =

5. Rock, paper, scissors
What is the probability that the first player will win a game of rock, paper, scissors?
Using the two-way table we can identify all the ways that the first player can win.
Scissors
Paper
Rock
First player
Second player SS SP SR PS PP PR RS RP RR SP PR
Remember the rules of the game:
Scissors beats paper; paper beats stone; stone beats scissors. RS 3 9 = 1 3
P(first player wins) =

6. Rock, paper, scissors
What is the probability that the second player will win a game of rock, paper, scissors,?
Using the two-way table we can identify all the ways that the second player can win.
Scissors
Paper
Rock
First player
Second player SS SP SR PS PP PR RS RP RR SR PS
Remember the rules of the game:
Scissors beats paper; paper beats stone; stone beats scissors. RP 3 9 = 1 3
P(second player wins) =

7. Rock, paper, scissors Is rock, paper, scissors a fair game? 1
P(first player wins) = 1 3
P(second player wins) = 1 3
P(a draw) = 1 3
Both player are equally likely to win so, yes, it is a fair game.
Review what is meant by a fair game. In a fair game all players are equally likely to win.
Allow pupils to play the game in pairs and to record their results.
Discuss the fact that in 30 games we would expect to get 10 wins for the first player, 10 wins for the second player and 10 draws. Discuss why this does not happen in reality.
Play rock, paper, scissors 30 times with a partner.
Record the number of wins for each player and the number of draws. Are the results as you expected?

8. Probability statements
Statements involving probability are often incorrect or misleading. Discuss the following statements:
The number 18 has been drawn the most often in the lottery so I’m more likely to win if I choose it.
I’ve just thrown four heads in a row so I’m much less likely to get a head on my next throw.
Discuss each statement in detail.
Many misconceptions arise in probability due to a failure to appreciate the random nature of independent events.
For example, for the second statement, if we assume that the coin is unbiased then the next throw is just as likely to come up heads than any other throw- the probability is ½- because the coin has no memory and the results are random.
It is true that it is very unlikely that five heads in a row would be thrown, however, we are not talking about the probability of getting five heads in a row, we are talking about the probability of the next throw being heads.
We could also argue that since it is unlikely that four heads would be thrown in a row the coin must be biased in some way. Based on the coins past history it could therefore be argued that the coin is actually more likely to land heads up.
For the last statement, this is only true if the meal served is random and that both curry and pizza are equally likely. If there is a choice involved then the only way to estimate the probability of the next person choosing curry is to carry out a survey to find out which meal people prefer. If 74 out of 100 people surveyed preferred pizza, for example, then we could estimate that the probability of the next person choosing pizza is 0.74 or 74%.
There are two choices for lunch, pizza or pasta. That means that there is a 50% chance that the next person will choose pizza.
I’m so unlucky. If I roll this dice I’ll never get a six.