Transcript Rock, paper, Scissors

Statistics and Probability
Rock, Paper, Scissors:
A Probability Experiment
Rock, paper, Scissors
In the game rock, paper, scissors two players have to show
either scissors, paper, or rock 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
S for Scissors, P for Paper and R for Rock.
Second player
First
player
Scissors
Paper
Stone
Scissors
SS
SP
SR
Paper
PS
PP
PR
Stone
RS
RP
TT
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
Stone
Scissors
SS
SP
SR
Paper
PS
PP
PR
PT
Stone
TS
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
First
player
Scissors
Paper
Stone
Scissors
SS
SP
SR
ST
Paper
PS
PP
PR
Stone
RS
TP
RP
RR
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?