Tree diagrams

Task goals

• Construct and read a two-stage probability tree diagram, where each branch is labelled with a probability and every pair of sibling branches sums to 1.
• List every possible outcome of two consecutive events (e.g. HH, HT, TH, TT) and find the probability of a combined outcome by multiplying the probabilities along its branches.
• Find a missing branch probability using the fact that probabilities leaving the same point sum to 1.
• Distinguish "with replacement" (independent events -- the second-stage probabilities are unchanged) from "without replacement" (dependent events -- the second-stage probabilities change because an item has been removed from the total).
• Find the probability of "at least one" outcome, or of an outcome occurring in either order, by combining (adding) more than one leaf's combined probability.