Venn Diagram Question

[mapmichelle]

A poll of student showed that 55 percent liked basketball, 40 percent liked soccer, 55 percent liked football, 25 percent liked both basketball and soccer, 20 percent liked both soccer and football, 20 percent liked both basketball and football, and 10 liked all three sports. Use a Venn Diagram to answer these questions: What percentage of students likes only one sport? What percentage does not like any of the three sports?

Please show you found the answer.

Thanks!

 

[tkhunny]

You had better get started. Did you draw the diagram?

The entire sports-liking population can be determined by the principle of Inclusion-Exclusion

(55% + 40% + 55%) - (25% + 20% + 20%) + (10%)