rock, paper, scissors

Rock, Paper, ScissorsA 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:

unlikely50-50

chance likely

possible

probable

certain

poor chance

impossible

very likely

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:

The rules of the game are that:

scissorspaperrock

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.


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

Scissors

Paper

Rock

First player

Second player

SS SP SR

PS PP PR

RS RP RR

P(same hands) =

SS

PP

RR

39

=13


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

Scissors

Paper

Rock

First player

Second player

SS SP SR

PS PP PR

RS RP RR

P(first player wins) =39

=13

SP

PR

RS


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

Scissors

Paper

Rock

First player

Second player

SS SP SR

PS PP PR

RS RP RR

P(second player wins) =39

=13

SR

PS

RP


Is rock, paper, scissors a fair game?

P(first player wins) =13

P(second player wins) =13

P(a draw) =13

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’ve just thrown four heads in a row so I’m much less likely to get a head on my next throw.

I’m so unlucky. If I roll this dice I’ll never get a six.

There are two choices for lunch, pizza or pasta. That means that there is a 50% chance that the next person will choose pizza.

rock, paper, scissors

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