You are to design a spinner for a game show that runs every
week night.
They are willing to give away the following prizes.
A New
House: One every 12 weeks.
A New
Car: One every 6weeks
A
Holiday: One every 4 weeks.
A New
Boat: One every 3 weeks
$10 000
Cash: Once every 2 weeks.
Sponsors
Prize: Twice per week
$1 000
Cash: Once per week
Wooden
Spoon: Remainder of games.
You are
to design and make a game show spinner that fits the above conditions. Show all
calculations.
What are the theoretical probabilities for each prize?
Spin your spinner 60 times and record the results.
Compare your theoretical and actual probabilities for your
spinner?

1.0

… Students recognise and respond to
unpredictability and variability in events, such as getting or not getting a
certain number on the roll of a die in a game or the outcome of a coin toss.

1.25

·
Awareness that some events are equally likely to
occur; for example, a head or a tail showing when a coin is tossed

1.75

· Ordering of
familiar events in terms of their probability between impossible andcertain

2.0

… Students predict the outcome of chance events,
such as the rolling of a die, using qualitative terms such as certain,
likely, unlikely and impossible.

2.5

·
Identification of events which are equally likely

3.0

… Students compare the likelihood of everyday
events (for example, the chances of rain and snow).
They describe the fairness of events in
qualitative terms.

3.25

·
Use of fractions to assign probability values
between 0 and 1 to probabilities based on symmetry; for example, Pr(six on a
die) = 1/6

4.0

… Students calculate probabilities for chance
outcomes (for example, using spinners) and use the symmetry properties of
equally likely outcomes.
They simulate chance events (for example, the
chance that a family has three girls in a row) and understand that
experimental estimates of probabilities converge to the theoretical
probability in the long run.

4.75

·
Use of random numbers to assist in probability
simulations and the arithmetic manipulation of random numbers to achieve the
desired set of outcomes
·
Calculation of theoretical probability using
ratio of number of ‘successful’ outcomes to total number of outcomes

5.0

… Students identify empirical probability as
longrun relative frequency.
They calculate theoretical probabilities by
dividing the number of possible successful outcomes by the total number of
possible outcomes.
They use tree diagrams to investigate the probability
of outcomes in simple multiple event trials.

6.0

Students estimate probabilities based on data
(experiments, surveys, samples, simulations) and assign and justify
subjective probabilities in familiar situations.

