Page 150 - MAT KS3 Y8 Cambridge CheckPoint

15 Probability

Do you know the game ‘rock, paper, scissors’? It is a very old game Key words
and is known by other names as well.
Make sure you learn and
Two people simultaneously show either a fist (rock), the first two
understand these key words:
fingers pointing forwards (scissors) or an open hand (paper).
at random
Scissors beats paper, paper beats rock and rock beats scissors. This mutually exclusive
is because scissors cut paper, paper wraps rock and rock blunts experimental probability
scissors.
theoretical probability
If both players choose the same thing it is a draw (neither wins) and
they play again.

This may seem a trivial game but in 2005 the Maspro Denkoh scissors
electronics corporation used it to decide whether to give beats paper
the contract to auction its $20 million collection of
paintings to Sotheby’s or to Christie’s auction houses.
Christie’s won with paper, after taking the advice of Flora
and Alice, the 11-year-old daughters of one of the directors paper
of the company. Their argument was that for beginners, beats rock
rock seems strongest, so they tend to start with that.
Playing against a beginner, you should start with paper.
This is a good example of when probabilities may not be
equally likely although they appear to be at first. It also rock
shows the (financial!) value of a sound logical argument. beats scissors
Auction houses typically take 10% of any money paid in
an auction.
This game illustrates two methods of finding probabilities.

One method is to say that each different play – rock, scissors, paper – is equally likely. Because there are
1
three outcomes (results), each one has a probability of .
3
However, this only works if each play is equally likely and the player chooses at random. Flora and Alice
1
realised that, for less experienced players, the probability of starting with rock is more than .
3
To find out what this probability actually is, you could do an experiment. You could teach the game to
lots of new players and then make a note of their moves. Then you could look at the fraction of times
they started with rock and that would give a value for the probability.
The first method, equally likely outcomes, gives a theoretical probability. The second method, doing an
experiment, gives an experimental probability. You will look at both of these in this unit.

148 15 Probability