Probability Tree Diagrams

Learn how to draw and use probability tree diagrams to work out probabilities step by step. Letโ€™s get started! ๐Ÿš€

Probability Tree Diagrams - introduction visual

Video Lesson

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Flashcards

Review key concepts visually

Red and blue balls with numbers 3 and 7 beside a bag of 10 balls, illustrating possible outcomes in a probability experiment.Probability tree diagram showing two-ball draws without replacement from a bag with 3 red and 6 blue balls.Probability tree diagram illustrating the drawing of 9 balls, 3 red and 6 blue, with dependent probabilities and combined event outcomes.Probability tree diagram for the calculation of drawing two balls of the same colour using equiprobable events and addition rule for probabilities.Probability tree diagram showing the calculation of drawing 2 balls of the same colour with red and blue ball probabilities, expected values.

๐Ÿ›Ž๏ธ What Is a Probability Tree Diagram?

  • A probability tree diagram shows all possible outcomes step by step.
  • It is used for two-stage events, like drawing one ball at a time.

๐Ÿ›Ž๏ธ Drawing the Probability Tree Correctly

  • Write fractions on every branch so probabilities are clear.
  • After the first outcome, update the probabilities for what is left.

๐Ÿ›Ž๏ธ Finding the Probability of a Single Outcome

  • You multiply the probabilities along one path.
  • This gives the probability of one specific result.

๐Ÿ›Ž๏ธ Finding the Probability of a Combined Event

  • A combined event means more than one path fits the question.
  • You add the probabilities of paths like redโ€“red and blueโ€“blue.

๐Ÿ›Ž๏ธ Probability of At Least One Event Happening

  • You can add all paths where the event happens.
  • Or do 1 โˆ’ probability of the opposite to save time and check your answer.

Practice Questions

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Interactive Activity

Use a tree diagram to visualize how probabilities are calculated.

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