Question

# A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did n

Two-way tables

A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-50s.

$$\begin{array} {lc} & \text{Soccer experience} \\ \text {Arthritis} &\begin{array}{l|c|c|c|c} & & & \text { Did not } & \\ & \text { Elite } & \text { Non-elite } & \text { play } & \text { Total } \\ \hline \text { Yes } & 10 & 9 & 24 & 43 \\ \hline \text { No } & 61 & 206 & 548 & 815 \\ \hline \text { Total } & 71 & 215 & 572 & 858 \end{array} \ \end{array}$$

Suppose we choose one of these players at random. What is the probability that the player has arthritis?

P(arthritis)= # of favorable outcomes # of possible outcomes$$=(10+9+24)/(10+61+9+206+24+548)=48/858 ~ 0.0501=5.01\%$$