# A sports psychologist performed a study of some visualization

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,  of the participants were golfers, and the other  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:  of the golfers reported a solid improvement in their performance after using the visualization techniques, and  of the tennis players reported a solid improvement in their performance after using the techniques.

Let  denote the event that a randomly chosen participant was a golfer and  denote the event that a randomly chosen participant was a tennis player. Let  denote the event that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques and  denote the event that a randomly chosen participant did not report 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. Do not round any of your responses.

=PIG

0.85

=P∩GI

=PG

=P∩GI

=PIG

=PIG

=P∩GI

=PG

0.6

=P∩GI

=PIG

0.3

What is the probability that a randomly chosen participant did not report a solid improvement in performance after using the visualization techniques?

(550 words)

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