Active.com cites a statistic that 80% of distance runners get injured in a given year. Among the main causes, one of the leading ones is poor core strength which leads to inadequate running form. Therefore, strength training is often recommended as a supplementary exercise for regular distance runners. Surveys have shown 2% of runners who choose to perform regular strength training will be injured in a given year, and 7% of runners who choose not to engage in regular strength training will not get injured.Hint:Start by drawing a Venn diagram.

1.What is the probability that a randomly chosen distance runner performs regular strength training?

a.0.80

b.0.20

c.0.15

d.0.13

e.0.87

2.Rounded to two digits, what is the probability that a randomly chosen distance runner will be injured given that the individual performs regular strength training?

a.0.02

b.0.13

c.0.87

d.0.15

e.0.20

3.Is injury independent of strength training? Why or why not?

a.Yes, because P(I and S) P(I) *P(S).

b.No, because P(I and S) P(I) *P(S).

c.Yes, because P(I and S) 0.

d.No, because P(I and S) 0.

e.Cannot be determined from the giveninformation.