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Calculate the probability of combined events using,where appropriate:• sample space diagrams• Venn diagrams• tree diagrams

Question

Calculate the probability of combined events using,where appropriate:• sample space diagrams• Venn diagrams• tree diagrams

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Solution

Sure, let's break down how to calculate the probability of combined events using sample space diagrams, Venn diagrams, and tree diagrams.

  1. Sample Space Diagrams:

    • First, list all possible outcomes of the event in a sample space diagram. This could be a list, a table, or a grid.
    • Then, identify the outcomes that represent the event you're interested in.
    • The probability of the event is the number of favorable outcomes divided by the total number of outcomes.

  2. Venn Diagrams:

    • Draw a rectangle to represent the sample space and circles within the rectangle to represent events.
    • Fill in the number of outcomes for each event in the corresponding circle. If an outcome belongs to more than one event, it should be placed in the intersection of the circles.
    • The probability of an event is the sum of the outcomes in its circle divided by the total number of outcomes in the sample space.

  3. Tree Diagrams:

    • Draw a tree diagram to represent all possible outcomes of the event. Each branch of the tree represents an outcome.
    • Write the probability of each outcome along the branch that represents it. The probabilities of all outcomes branching from the same point should add up to 1.
    • To find the probability of a combined event, multiply the probabilities along the branches that lead to it.

Remember, the probability of an event is always between 0 and 1, inclusive. A probability of 0 means the event is impossible, and a probability of 1 means the event is certain.

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