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 90% of the golfers reported a solid improvement in their performance after using the visualization techniques, and s5% of the tennis players reported a solid improvement in their performance after using the techniques. Let a denote the event that a randomly chosen participant was a golfer and 6 denote 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 7 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. (If necessary, consult a list of formulas.) r(4|0) - r(0) P(a n 7)- O 0.1 0.85 r(7) - 03 (7|7) - What is the probability that a randomly chosen participant reported a solid improvement in performance after using the visualization techniques? ?

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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O PROBABILITY
Tree diagram.
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:
90% of the golfers reported a solid improvement in their performance after
using the visualization techniques, and s5% 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
G denote 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 7
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.
(If necessary, consult a list of formulas.)
P(1|G) =
P(G n 1) -
P(6) -
p(G n 7) - 0
P(ī|6) -
0.1
0.85
P(ūni) - 0
PG) - 0.3
P(anī) -
P(7|7) -
What is the probability that a randomly chosen participant
reported a solid improvement in performance after using
the visualization techniques?
Explanation
Check
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Given:

Let G denote the event that the randomly chosen participant was a golfer and $G$ denote the event that the randomly chosen participant was tennis player.

Let I denote the event that the randomly chosen participant reported a solid improvement in performance after using the visualization techniques and $I$ denote the event that the randomly chosen participant did not report a solid improvement in performance after using the visualization techniques.

$P (G) = 0.7 P (\bar{G}) = 0.3 P (I | G) = 0.9 P (I | \bar{G}) = 0.85$

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