Question

2. The table below shows the number of athletes who stretch before exercising and how many had injuries in the last year: Injury in the last year Stretching? Yes No Yes 55 295 No 231 219 (a) What is the risk of injury if an athlete stretches before exercising? (b) What is the risk of injury if an athlete doesn't stretch before exercising? (c) What is the relative risk of an injury for athletes who didn't stretch compared to athletes who did? Interpret this result.

Answer 1

Given table shows the number of athletes who stretch before exercising and how many had injuries in the last year. The table is as follows :

	Injury in the last year
Stretching?	Yes No	Total
Yes	55 295	350
No	231 219	450
Total	286 514	800

We know, Probability of any event = (Number of favorable outcomes)/(Total number of possible outcomes) ------(1)

From the table, Total number of athletes = 800. Thus, total number of possible outcomes = 800. --------(2)

a) Here, we have to find the risk of injury if an athlete stretches before exercising. Number of athletes who got injury inspite of doing stretching before exercise = 55. Thus, number of favorable outcomes = 55 .

Thus, from (1) and (2), the required probability = 55/800 = 0.06875 .

Thus, the risk of injury if an athlete stretches before exercising = 0.06875 .

b) Here, we have to find the risk of injury if an athlete doesn't stretch before exercising. Number of athletes who got injury for not doing stretching before exercise = 231. Thus, number of favorable outcomes = 231 .

Thus, from (1) and (2), the required probability = 231/800 = 0.28875 .

Thus, the risk of injury if an athlete doesn't stretch before exercising = 0.28875 .

c) Here, we have to find the relative risk of an injury for athletes who didn't stretch compared to athletes who did. We know, relative risk = (Probability of event A)/(Probability of event B). Here, the event of risk of injury for athletes who didn't stretch be the event A and the event of risk of injury for athletes who did stretch be the event B.

From parts (a) and (b), P(A) = 0.28875 and P(B) = 0.06875.

Thus, the relative risk = P(A)/P(B) = 0.28875/0.06875 = 4.2 .

Thus, the relative risk of an injury for athletes who didn't stretch compared to athletes who did = 4.2 .