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AS 3.13 Achievement Objectives

Excellence

• Apply probability concepts in solving problems.

• Apply probability concepts, using relational thinking, in solving problems.

• Apply probability concepts, using extended abstract thinking, in solving problems.

This involves involves one or more of:
- selecting and using methods,
- demonstrating knowledge of concepts and terms,
- communicating using appropriate representations.

This involves involves one or more of:
- selecting and carrying out a logical sequence of steps,
- connecting different concepts or representations,
- demonstrating understanding of concepts;

and also relating findings to a context or communicating thinking using appropriate statements.

This involves involves one or more of:
- devising a strategy to investigate or solve a problem,
- identifying relevant concepts in context'
- developing a chain of logical reasoning,
- making a generalisation;

and also where appropriate, using contextual knowledge to reflect on the answer.

Problems are situations that provide opportunities to apply knowledge or understanding of mathematical and statistical concepts and methods.
Situations will be set in real-life or statistical contexts. (Well there's a surprise)

This means you have to know about:
- true probability versus model estimates versus experimental estimates
- randomness
- independence
- mutually exclusive events
- conditional probabilities
- probability distribution tables and graphs
- two way tables
- probability trees
- Venn diagrams.

Clarifications from NZQA Specifications page (Class notes)

Probabilities may be expected to be calculated from formulae, a probability distribution table or graph,
tables of counts or proportions, simulation results or from written information. Candidates should
clearly show the method they have used to calculate probabilities and state assumptions made.

Candidates may be required to interpret solutions in context.
Sensible rounding is expected. Early rounding may be penalised.

Curriculum Achievement Objective

Details about the NEW Standard: From http://new.censusatschool.org.nz/resources/3-13/
This standard is derived from Achievement Objective S8.4,
- Investigate situations that involve elements of chance
- calculating probabilities of independent, combined and conditional events
Students should be able to:
Understand true probability vs model estimates vs experimental estimates
Randomness, independence mutually exclusive events, conditional probability
Probability distribution tables and graphs
Two way tables, probability tress, venn diagrams
This standard requires students to understand the relationship between true probability, model estimates, and experimental estimates.

NZC Level 8: from : http://new.censusatschool.org.nz/key-ideas/probability/#level8
The key idea of probability at Level 8 is investigating chance situations using probability concepts and distributions.

At Level 8 students are investigating chance situations using concepts such as
- randomness,
- probabilities of combined events and mutually exclusive events,
- independence,
- conditional probabilities
- expected values and standard deviations of discrete random variables,

Students should know the three different types of chance situations which can arise

Good model: An example of this is the standard theoretical model for a fair coin toss where heads and tails are equally likely with probability ½ each. Repeated tosses of a fair coin can be used to estimate the probabilities of heads and tails. For a fair coin we would expect these estimates to be close to the theoretical model probabilities.

No model: In this situation there is no obvious theoretical model, for example, a drawing pin toss. Here we can only estimate the probabilities and probability distributions via experiment. (These estimates can be used as a basis for building a theoretical model.)

Poor model: In some situations, however, such as spinning a coin, we might think that the obvious theoretical model was equally likely outcomes for heads and tails but estimates of the outcome probabilities from sufficiently large experiments will show that this is a surprisingly poor model. (Try it! Another example is rolling a pencil.) There is now a need to find a better model using the estimates from the experiments.
Link to statistical investigations: Students are exploring outcomes for single categorical variables in statistical investigations from a probabilistic perspective.