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Year 10 Mathematics
Probability
Chapter 4
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RESTS ON
Percent as parts per hundred
CH 2
Multiply and divide fractions
CH 2
Complete and validate a finite probability assignment: every probability is non-negative and the total is exactly one; use stated unequal outcome masses rather than assuming equiprobability
FOUNDATIONS
Build a frequency table for categorical data
CH 5
Classify a numerical variable as discrete or continuous
CH 5
Distinguish an element statement from a subset statement and decide whether a finite set is contained in another stated set
FOUNDATIONS
Name the explanatory and response variables from the direction of the question asked
CH 5
Classify a bivariate question as categorical–categorical, numerical–categorical or numerical–numerical
FOUNDATIONS
Probability scale and experiments
Venn diagrams and sets
Two-way tables
Conditional probability
Two-step sample spaces
Tree diagrams
Independence and simulations
Place a probability on the 0–1 chance scale, name its qualitative band and order probability expressions written in different equivalent forms by value
Equivalent fractions
Convert a fraction to a percentage
Decimal place value
Multiplication and division
Distinguish a random experiment, one outcome, the full sample space and an event as a subset of that sample space
Construct or recognise a complete finite sample space, preserving order where successive stages make ordered tuples distinct
For equiprobable outcomes, calculate an event probability as favourable outcomes divided by all outcomes and verify that it lies from zero to one
Obtain the probability of the complement as one minus the event probability and interpret impossible and certain boundary cases
Interpret unions, intersections and complements as “at least one”, “both”, “only”, “neither” and related event descriptions relative to a stated sample space
Simplify a fraction
Calculate an estimated probability as the exact success count over trial count and interpret repeated-run variation without claiming that a finite simulation equals the theoretical probability
Build a frequency table for discrete numerical data
Choose a random device, outcome mapping, replacement rule, repetition unit and success condition that simulate the stated experiment without changing its probabilities
Determine whether events can occur together and use the zero-intersection special case of the addition rule without confusing exclusivity with independence
Form or recognise the union, intersection, difference and complement of finite or interval-defined sets relative to an explicitly stated universe
Calculate a union by adding the marginal probabilities and subtracting the intersection once
Complete and read a two-event count or probability table, including four interior regions, row and column margins and the grand total
Construct and read a two-way frequency table from paired categorical records
Interpret the event after the conditioning event is known and restrict the denominator to that event's outcomes or table margin
Calculate an exact conditional probability as the intersection probability divided by the conditioning-event probability, with a nonzero conditioning event
Rearrange the conditional formula to calculate an intersection as a first-stage probability times the appropriate conditional probability
Represent a two- or three-stage finite experiment by an ordered list, grid, table or tree and count its elementary outcomes without collapsing ordered outcomes
Multiply the number of choices at successive stages for an AND procedure, updating later choices when repetition is forbidden
Read or complete a two- or three-stage probability tree: sibling branch probabilities sum to one, a path probability is the product along that path and alternative terminal paths are added
Partition an event across exhaustive first-stage cases and add the exact path probabilities to obtain its marginal probability
Determine whether two events are independent by checking either conditional invariance or the exact product equality for the intersection