Final answer:
To calculate the probability of an athlete stretching before exercising, divide the number of athletes who stretch by the total number of athletes. For the conditional probability of an athlete stretching given no injuries in the last year, divide the number of athletes who stretch without injuries by the number with no injuries.
Step-by-step explanation:
To answer the questions related to the provided data, we need to use the concepts of probability. Let's assume Table 3.4 has the information required to solve these queries.
a. What is P(Athlete stretches before exercising)?
The probability that an athlete stretches before exercising, P(Athlete stretches before exercising), is calculated by dividing the number of athletes who stretch before exercising by the total number of athletes surveyed. If we denote the number of athletes who stretch as ‘S’ and the total number of athletes as ‘T’, the formula would be:
P(Athlete stretches before exercising) = S / T
b. What is P(Athlete stretches before exercising|no injury in the last year)?
The conditional probability that an athlete stretches before exercising given that there was no injury in the past year, P(Athlete stretches before exercising|no injury in the last year), is found by dividing the number of athletes who stretch and have had no injuries by the number of athletes who have had no injuries. If ‘SN’ represents athletes who stretch and had no injuries, and ‘N’ represents the athletes with no injuries, the formula is:
P(Athlete stretches before exercising|no injury in the last year) = SN / N