Tree Diagrams

Tree Diagrams

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Tree Diagrams

• Tree diagrams are visual representations of all the possible outcomes of a sequence of events.
• They are particularly useful in determining conditional probabilities.
• Each ‘branch’ on the tree represents an outcome.
• The probability of each outcome is written on the branch and the ends of the branches represent outcomes.
• The sum of the probabilities in each branch is always 1.

Independent Events

• When the outcome of an event does not affect the outcome of another, these events are independent.
• The probability that two independent events will occur is the product of their respective probabilities.

Dependent Events

• When the outcome of one event does affect the outcome of another, these events are dependent.
• For dependent events, we modify the calculation of the probability that both happen, often using a tree diagram to understand the situation.

Conditional Probability

• Conditional probability is the probability that event B happens, given that event A has already happened.

• Notated as P(B

  A), read as “probability of B given A”.

Pictorial Representation

• The sample space for a sequence of events can get complex, tree diagrams aid visual understanding.
• By working from left to right, one can clearly see the progression of all potential outcomes.

Remember to practice a variety of problems involving independent and dependent events, as well as conditional probability, so you can solidify your understanding of these principles and apply them appropriately.