Analyzing Sports Preferences in Class A

The question asks for the maximum possible percentage of students in Class A who do not like to play any of the four given games: cricket, tennis, handball, and football. We are provided with the percentage of students in Class A who like each specific game.

Understanding the Data for Class A

Let's extract the relevant data for Class A from the table:

Note that the percentages represent the proportion of students in Class A who like a particular game. A student can like more than one game, or no game at all. This means the groups of students who like different games might overlap.

Finding the Maximum Percentage Not Liking Any Game

We want to find the maximum percentage of students who like *none* of the four games. To maximize the group who like none, we must minimize the group who like *at least one* game.

Consider the percentages of students who like each game in Class A:

• Cricket: 60%
• Tennis: 70%
• Handball: 50%
• Football: 60%

The percentage of students who like *at least one* game is the union of the sets of students who like each game. The minimum possible size of this union occurs when the sets overlap as much as possible. The largest individual percentage is 70% (for Tennis). This means that 70% of students like Tennis. It is possible, in the scenario where the union is minimized, that all students who like Cricket (60%), Handball (50%), and Football (60%) are also included within the 70% who like Tennis.

Therefore, the minimum percentage of students who like at least one game is the maximum of the individual percentages:

\(\text{Minimum percentage liking at least one game} = \max(60\%, 70\%, 50\%, 60\%) = 70\%\)

If the minimum percentage of students who like at least one game is 70%, then the maximum percentage of students who do *not* like any of the games is the complement of this value.

\(\text{Maximum percentage not liking any game} = 100\% - \text{Minimum percentage liking at least one game}\)

\(\text{Maximum percentage not liking any game} = 100\% - 70\%\)

\(\text{Maximum percentage not liking any game} = 30\%\)

This represents the scenario where the 70% of students who like Tennis potentially include all students who like other sports, leaving the remaining 30% as those who like none of the listed games.

Conclusion

Based on the data for Class A, the maximum percentage of students who do not like to play any of the given four games is 30%.

The final answer is 30%.

Revision Table: Class A Sports Data

Additional Information: Understanding Overlapping Sets and Percentages

When dealing with percentages for different categories that can overlap (like students liking different sports), the sum of the percentages can exceed 100%. This is because students are counted in multiple categories if they like more than one sport.

• To find the minimum percentage of students who like *at least one* item from a set of categories with given percentages (allowing overlap), you take the maximum of the individual percentages. This assumes that the groups liking the smaller-percentage items are entirely contained within the group liking the largest-percentage item.
• To find the maximum percentage of students who like *none* of the items, you subtract the minimum percentage who like *at least one* item from 100%. This represents the remaining students who are not part of the smallest possible union of the categories.

This method gives the bounds (minimum/maximum) for the number/percentage of students in the union or its complement when the extent of overlap between categories is unknown but students can belong to multiple categories.