First, represent the information on a tree diagram: From the tree diagram, the probability of winning the second set = \(\frac{27}{50} + \frac{10}{50} = \frac {37}{50}\). Tree Diagrams, like Venn Diagrams, provide a simple visual way of representing events and their associated probabilities.They can be used to calculate more complicated probabilities. Tree Diagrams display the probabilities different event outcomes on the ‘branches’ of the diagram. Tree diagrams can be used to visualize and solve conditional probabilities. Once the sample space is illustrated, the tree diagram can be used for detennining probabilities. This type of diagram can be very useful for some problems. Remember that: P(A and B) = P(A) x P(B|A) Here is how to do it for the "Sam, Yes" branch: (When we take the 0.6 chance of Sam being coach times the 0.5 chance that Sam will let you be Goalkeeper … Worked examples. Tree diagrams consist of "branches" that are labeled with either frequencies or probabilities.The following example illustrates how Tree Diagram in Probability. Fig.1.23 - A tree diagram. Consider two archers firing simultaneously at a target. In this figure, we obtain the probability at each point by multiplying probabilities on the branches leading to that point. Use a tree diagram: Probability of a red sheet of paper being chosen. We can interpret this formula using a tree diagram such as the one shown in Figure 1.23. Tree Diagrams in Conditional Probability Sometimes, when the probability problems are complex, it can be helpful to graph the situation. Conditional Probability and Tree Diagrams Here we are estimating the probability that LeBron will make the eld goal given the extra information that the attempt will be made in a game after 3 days + rest. The tree diagram is complete, now let's calculate the overall probabilities. 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