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Researchers interviewed athletes about their most recent workout. They found that 90% of athletes did not suffer an injury while working out, 58% stretched before

Researchers interviewed athletes about their most recent workout. They found that 90% of athletes did not suffer an injury while working out, 58% stretched before working out, and 55% stretched and did not suffer an injury.

Fill in the probability table below.

(Round to two decimal places.)

Stretched:------------------------ Didn't Stretch:----------------------------------- TOTAL:-------------------------

Injury: ----------------------------------------, -----------------------------------------------------,---------------------------------

No Injury: ------------------------------------,------------------------------------------------------,----------------------------------

TOTAL:---------------------------------------,------------------------------------------------------,------------------------------------

a. What is the probability that a randomly selected athlete did not stretch before working out?

b. What is the probability that a randomly selected athlete was injured?

c. Of the athletes who were injured, what is the probability that they didn't stretch before working out?

d. Are stretching and suffering an injury independent? Justify your answer.

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