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-fifties:

(a) What percent of the people in this study were elite soccer players? What percent had arthritis?

(b) What percent of the elite soccer players had arthritis? What percent of those who had arthritis were elite soccer players?

Given table :

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The two-way tables demonstrate the dangers of playing soccer for individuals based on whe10ther or not they had arthritic hips or knees by the time they were in their fifties.

Individuals who were elite players, no-elite players and those who did not play soccer were classified in a two-way table.

$$\begin{gathered} =\frac{totalnumberofelitesoccerplayers}{totalnumberofsoccerplayers} \\ =71/858 \end{gathered}$$

Number of professional soccer players=$$\begin{gathered} =0.082751 \\ =0.0828 \\ =8.28\% \end{gathered}$$

$=\frac{totalnumberofarthritis}{totalnumberofsoccerplayers}$

Proportion of arthritis$$\begin{gathered} =\frac{43}{858} \\ =0.050117 \\ =5.01\% \end{gathered}$$

As a result, the percentages of elite soccer players with arthritis are $8.28$percent and $5.01$percent, respectively.

The percentage of elite soccer players who had arthritis was high.

$$\begin{gathered} \left(proportionofarthritiswereelitesoccerplayers\right)=\frac{\left(totalnumberofarthritiswereelitesoccerplayers\right)}{\left(totalnumberofarthritis\right)} \\ =1043 \\ =0.2326 \\ =23.26\% \end{gathered}$$

Elite soccer players have the highest rate of arthritis.

As a result, $23.26$ percent of those with arthritis were top soccer players, and $14.08$ percent of those with arthritis were elite soccer players.