Tree Diagrams Sometimes, when probability problems seem to be more complex, it can be helpful to graph the scenario. Tree diagrams and Venn diagrams are two tools that are used to visualize and solve conditional probabilities. Tree Diagrams Definition A tree diagram is a special type of graph used to determine the outcomes of an experiment. It consists of branches that are labeled with either frequencies or probabilities. Example 3.21 Let's take Example 3.14, where we tossed a coin twice. Recall the sample space {T T, T H, HH, HT} Draw a tree diagram representing this sample space. Find the probability for tossing more than one tail. 1. Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. What is the probability that her luggage arrives in Denver with her? 2. Suppose that 23% of adults smoke cigarettes. It's known that 57% of smokers and 13% of non- smokers develop a certain lung condition by the age of 60. What is the probability that a randomly selected 60-year-old has this lung condition? Tree Diagrams Examples: Intuitive Bayes' Theorem : Assume some convenient value for the total of all items involved, then construct a table of rows and columns with the individual cell frequencies based on the known prob