Each afternoon there is a 85% chance that Pippin and I will go for a walk. If we do go for a walk, there is a 25% chance that I will throw a ball for her at the park. If we do not go for a walk, I will definitely throw a ball for her to chase in the house. (a) Draw and label a tree diagram to represent the outcomes of the experiment. (b) On a given day, what is the probability that Pippin gets to chase a ball (either at the park or at home)? (c) If Pippin did get to chase a ball one day, what is the probability she did so at the park (since we went for a walk)? (d) Determine whether the events "Pippin and I go for a walk" and "Pippin gets to chase a ball" are independent. Explain your answer mathematically using a principle or formula from class.

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.