Tree Diagrams

  • Tree Diagrams are useful tools in probability theory to visualise and calculate the probability of different outcomes in a sequence of S events.

  • The branches of the tree symbolise possible outcomes. At the end of each branch, you will find the probability of that outcome occurring.

  • The probability of an outcome is a fraction between 0 and 1. It’s calculated by dividing the favourable outcomes by possible outcomes.

  • The sum of all outcome probabilities for a specific event will always add up to 1.

  • Outcomes are independent if the outcome of one event does not influence the outcome of another event. If the events are independent, then the probability of both events occurring is calculated by multiplying the probabilities of each event.

  • On the other hand, if events are dependent, the probability of the second event may be influenced by the result of the first event.

  • To calculate the total probability of an event along a specific path in the tree, multiply the probabilities along the branches of that path.

  • To calculate the total probability of a specific event happening over all possible ways it can occur, add the probabilities of all the paths that lead to that event occurring.

  • The tree diagram often includes complement events, those that represent all other possibilities other than the event under consideration. The probability of the complementary event is calculated by subtracting the probability of the event from 1.

  • To create a tree diagram, first identify the initial event and its possible outcomes. Write these as branches coming from a point. Then, from each branch, draw further branches for the next event and its possible outcomes. Continue until all sets of outcomes have been represented.

  • Make sure to label each branch with its corresponding probability and to specify which event each branch represents.

  • Tree Diagrams can be especially advantageous when tackling compound events, as they help to keep track of different stages and outcomes visually. They are also beneficial when mapping dependent events.