Statistics: Probability
Level 1
AO1: Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes. This means students will consider the possible outcomes of events. Possible outcomes can be listed, for example when tossing a coin the outcomes are heads and tails. The possible outcomes should be the basis for predictions rather than perceptions of luck.
Click to download a PDF of second-tier material relating to Level 1 Probability (125KB)
Level 2
AO1: Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty. This means students will recognise that probability is about the chance of outcomes occurring. Through activities that involve them personally, students at Level Two are expected to consider the possible outcomes of events in predicting what might occur. Through carrying out experiments, e.g. playing a game of chance, and making simple models of all the outcomes, e.g. lists or tables, students should recognise when outcomes appear to be equally likely, e.g. getting an even number when tossing a dice. Students should also recognise that where an event has more than one possible outcome they cannot predict the outcome with certainty, e.g. "it probably won’t be a six but it might be" when rolling a dice. Students should relate probability to events in their daily life, e.g. "it is very likely to rain today".
Click to download a PDF of second-tier material relating to Level 2 Probability (74KB)
Level 3
AO1: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary. This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. The chance is of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, e.g. tossing a coin ten times, vary from one another, and from the proportions expected from a model, i.e. most times five heads do not come up.
Click to download a PDF of second-tier material relating to Level 3 Probability (116KB)
Level 4
AO1: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), e.g. Take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample.
AO2: Use simple fractions and percentages to describe probabilities. Simple fractions and percentages in this objective are common benchmarks like one half (50%), thirds (33.3% and 66.6%), quarters (25% and 75%), fifths (20%, 40%, 60%, 80%), tenths (10%, 30%, etc). Students should know that outcomes that are certain are described by fractions equalling one, including 100%, and outcomes that are impossible are described by fractions equalling zero, including 0%. In contrived situations involving elements of chance, e.g. totalling two dice, students should know that the count of all possible outcomes gives the denominator of a probability fraction, e.g. 36 possible outcomes, and the number of desired outcomes gives the numerator, e.g. there are 9 ways to get a total of either 2,4 or 6 so the probability is 9/36 or 1/4 . In realistic situations where probabilities are estimated, e.g. the chance of a drawing pin landing safe, students are expected to accept variation from an exact fraction, e.g. 37 out of 100 were safe which is about or 33.3%..
Click to download a PDF of second-tier material relating to Level 4 Probability (154KB)
Level 5
AO1: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. Further detail on this Achievement Objective will be added shortly.
AO2: Calculate probabilities, using fractions, percentages, and ratios. Further detail on this Achievement Objective will be added shortly.
Level 6
AO1: Investigate situations that involve elements of chance:
Further detail on this Achievement Objective will be added shortly.
