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Foundation plus - Probability
infoWhy this? Representing chance through two-way tables, sample spaces, Venn diagrams, and tree diagrams helps us organise outcomes and calculate probabilities systematically. Reasoning about combined events and conditional probabilities develops our ability to interpret uncertainty and risk rather than rely on intuition.
scheduleWhy now? Introducing probability at the start of Year 10 establishes structured approaches to organising information and solving multi-stage problems. Work with tables and frequencies also provides representations that we revisit and extend in the later tables, charts, and graphs unit.
neurologyYou need to know
- A two-way table displays the frequencies of two categorical variables and can be used to find totals and probabilities.
- The probability of an event is calculated as the number of successful outcomes divided by the total number of possible outcomes.
- A sample space diagram lists all possible outcomes of two events, often using a grid or table.
- Probability notation includes ( P(A) ) for the probability of event A, ( P(A Ո B) ) for the probability of both A and B, and ( P(A Ս B) ) for the probability of A or B.
- Mutually exclusive events are events that cannot happen at the same time, and for such events, ( P(A Ս B) = P(A) + P(B) ).
- A Venn diagram is used to represent sets and their relationships, including intersections (( Ո )), unions (( Ս )), and complements (( A' )).
- A tree diagram is used to show all possible outcomes of a sequence of events and their associated probabilities.
- Conditional probability is the probability of one event occurring given that another event has already occurred, denoted as ( P(A|B) ).
rocket_launchYou must be able to
- Copy and complete a two-way table given partial data.
- Find probabilities of single and combined events using a two-way table.
- List all possible outcomes of two events using a sample space diagram.
- Find probabilities of events using a sample space diagram.
- Use probability notation correctly in calculations and explanations.
- Identify mutually exclusive events and calculate their combined probabilities.
- Copy and complete a Venn diagram given information about sets and their intersections.
- Find probabilities of events using a Venn diagram, including unions, intersections, and complements.
- Copy and complete a tree diagram for two-stage events.
- Find probabilities of outcomes using a tree diagram, including the probability of combined events.
- Calculate and interpret conditional probabilities, including using tree diagrams and the conditional probability formula.
Revision Quiz
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