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Probability, grade 9

Ninth-grade probability.Subjects

The topics, in order:

  • an experiment, its outcomes and events;
  • calculating a probability when the outcomes are equally likely, and the complement;
  • probability and relative frequency: what happens when an experiment is repeated many times;
  • two-stage experiments: the outcome table and the tree diagram;
  • drawing with and without putting back;
  • the area model.

Two kinds of lessons:

  • learning lessons – an explanation, solved examples and a few questions to try;
  • practice lessons – questions only.

How the page works: Using a page.

  1. Experiments, outcomes and eventsLearningAn experiment whose result is not known in advance, the sample space, an event, a certain event and an impossible event.
  2. The probability of equally likely outcomesLearningAn event's probability when all the outcomes are equally likely: the number of its outcomes over the number of all the outcomes; a number from 0 to 1; and outcomes that are not equally likely.
  3. The complement of an eventLearningThe complement – "the event does not happen": the other outcomes; its probability is 1 minus the event's; and when it is easier to calculate through it.
  4. Relative frequency and probabilityLearningThe relative frequency of an event, how it comes near the probability when an experiment is repeated many times, and estimating a probability with experiments.
  5. Practice: one-stage experimentsPracticeThe sample space, events, probability, the complement and relative frequency – and a statistics review: the frequency table, mode, mean and median of an experiment's outcomes.
  6. Two-stage experiments: the outcome tableLearningAn experiment in two stages – two dice, a coin and a die, a spinner spun twice: its outcomes in a table, and an event's probability from the number of its cells.
  7. The tree diagramLearningA two-stage experiment as a tree diagram: a probability on each branch, a path's probability as a product, an event of several paths, and "at least once" by the complement.
  8. Drawing with and without putting backLearningTwo marbles drawn from a bag: with putting back – the second draw is like the first; without – the second depends on the marble drawn. The same question both ways, and a draw in class.
  9. The area modelLearningA two-stage experiment as a square of area 1: strips for the first stage, cuts for the second, and an event's probability – the sum of its rectangles' areas.
  10. Practice: two-stage experimentsPracticeTwo-stage experiments in an outcome table, a tree diagram and an area model: with and without putting back, the complement, and mixed questions.
  11. Review: probability and statisticsPracticeA review of the whole course – events, probability, the complement, relative frequency, two-stage experiments – and of the frequency table: the mean, the median and the mode.
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