Rock, Paper, Scissors
A Probability Experiment
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:
unlikely
possible
50-50
chance
certain
likely
poor
chance
very
likely
impossible
probable
even
chance
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.
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.
Second player
First
player
Scissors
Paper
Rock
Scissors
SS
SP
SR
Paper
PS
PP
PR
Rock
RS
RP
RR
3
1
P(same hands) =
=
9
3
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.
Second player
First
player
Scissors
Paper
Rock
Scissors
SS
SP
Paper
PS
PP
SR
PR
Rock
RS
RP
RR
3
1
P(first player wins) =
=
9
3
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.
Second player
Scissors
Paper
Rock
SP
SR
SR
Paper
SS
PS
PP
PR
Rock
RS
RP
RR
Scissors
First
player
3
1
P(second player wins) =
=
9
3
Rock, paper, scissors
Is rock, paper, scissors a fair game?
P(first player wins) =
1
3
1
P(second player wins) =
3
1
P(a draw) =
3
Both player are equally likely to win so, yes, it is a fair game.
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?
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’m so unlucky. If
I roll this dice I’ll
never get a six.
I’ve just thrown four heads in a
row so I’m much less likely to
get a head on my next throw.
There are two choices for lunch,
pizza or pasta. That means that
there is a 50% chance that the
next person will choose pizza.