Tree diagram for finding the probability of an event.

A sports psychologist performed a study of some visualization techniques that she developed to improve athletic performance. She used amateur golfers and amateur tennis players as participants. In her study 70% of the participants were golfers, and the other 30% were tennis players. (No participant was both a golfer and a tennis player.) The visualization techniques seemed quite helpful for both the golfers and the tennis players: 85% of the golfers reported a solid improvement in their performance after using the visualization techniques, and 75% of the tennis players reported a solid improvement in their performance after using the techniques.

Let G denote the event that a randomly chosen participant was a golfer and let the complement of G be the event that a randomly chosen participant was a tennis player. Let I denote the event that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques and let the complement of I be the event that a randomly chosen participant did not report a solid improvement in performance after using the visualization techniques.

What is the probability that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques?

Fill in the probabilities to complete the tree diagram below, and then answer the question that follows.

Using a tree diagram to find the probability of an event. The solution to this problem uses the formulas for complimentary events and for intersections of events.

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