3.13
Apply probability concepts in solving problems
Probability
External
AS91585
New focus
3.13 Expected Prior Knowledge

3.13 Lesson Log

3.13 Summary
3.13 Venn Diagrams
3.13 Tree Diagrams
3.13 Independence and Dependence
3.13 Arrangements Combinations Permutations
3.13 Risk
3.13 Conditional Probability
3.13 Probabilities from tables
3.13 Models Experiments Actual Probability
3.13 Deterministic vs Probabilistic
3.13 Randomness
3.13 Sample Paper Video Answers
3.13 Nulake Sample Student Answers
3.13 Practise Exam
Check for misconceptions with this quiz http://www.teacherlink.org/content/math/interactive/probability/interactivequiz/question1/home.html







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The Standard, Sample paper and answers
http://www.nzqa.govt.nz/ncea/assessment/view-detailed.do?standardNumber=91585
is the actual standard
is the answer schedule
is the practise paper
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Link to teaching resources http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-4
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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

(True Probability: heads does not have exactly 0.5 probability,)
(Model Estimates: excel simulation is one type of model, assume the probability of getting a head = 0.5)
(Experiments: actually toss the coin.)
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.
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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,
- probability distributions including the Poisson, binomial and normal distributions.
Students need to be able to model chance situations using both discrete and continuous probability distributions and apply probability concepts. They are using theoretical model probabilities and estimating probabilities from experiments as appropriate.

Students should know the three different types of chance situations which can arise (from NZC Level 3):
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.