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Probability tree diagrams

4 Rules for working with probability tree diagrams:

 

  1. Multiply the numbers along the branches to get the end results
  2. The numbers on any set of branches which all meet together at a point must always add up to 1
  3. Check probability tree diagrams are correct by making sure that the end results add up to 1
  4. To find the answer to a question, add up the relevant end results

4 things to remember:

  1. Break the question down into a sequence of separate events. For example, 3 dice are thrown, what is the probability that all 3 land on even numbers? Split this down into three separate throws
  2. You don’t always need to draw complete probability tree diagrams. Sometimes you need only draw the relevant parts of a tree
  3. Look out for conditional probabilities. For example, if two cards are chosen at random from a pack of cards, provided that the first card is returned before the second card is chosen then there are no conditional probabilities. If the first card is not returned to the pack, then the choice of second card is affected by the choice of first card, so the probabilities for the second card are conditional.
  4. If asked ‘at least’ type questions, such as ‘What is the probability of choosing at least one yellow ball?’, the easiest way is to work out 1 – Probability of the other outcome. So, ‘What is the probability of choosing at least one yellow ball?’ becomes 1- probability of no yellow ball

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