Table $3.3$shows the number of athletes who stretch before exercising and how many had injuries within the past year.

a. What is P (athlete stretches before exercising)?

b. What is P (athlete stretches before exercising|no injury in the last year)?

The table shows the number of athletes who stretch before exercising and how many had injuries within the past year.

The total number of athletes $=800$

Total number of athletes who stretch before exercise $=350$

The formula for P (athlete stretches before exercising) is :

role="math" localid="1649264437321" $$\begin{gathered} P\left(\text{athlete stretches before exercising}\right)=\frac{\text{athletes who stretch}}{\text{Total number of athletes}} \\ =\frac{350}{800} \\ =0.4375 \end{gathered}$$

The total number of athletes who have no injury in the last year $=514$

Out of athletes that have no injury last year, total number of athletes who stretches $=295$

The formula for P (athlete stretches before exercising|no injury in the last year) is :

$$\begin{gathered} P\left(\text{athlete stretches before exercising|no injury in the last year}\right)=\frac{295}{514} \\ =0.574 \end{gathered}$$