2. 7472 people were surveyed about which sport they liked the best. 584 liked US Football, 639 liked soccer and 523 liked Lacrosse. If 243 liked all three 181 liked football and soccer, as liked soccer and lacrosse. You must draw a Venn 77 liked football and Lacrosse and __ Diagram on the back to answer the questions.

To solve this problem, we need to use the information given to fill in the Venn diagram and then answer the questions.<br /><br />Let's start by filling in the Venn diagram:<br /><br />1. The total number of people surveyed is 1472.<br />2. 584 people liked US Football.<br />3. 639 people liked soccer.<br />4. 523 people liked Lacrosse.<br />5. 243 people liked all three sports.<br />6. 181 people liked football and soccer.<br />7. 217 people liked soccer and Lacrosse.<br />8. 77 people liked football and Lacrosse.<br /><br />Now, let's fill in the Venn diagram:<br /><br />- In the center circle, we have 243 people who liked all three sports.<br />- In the left circle, we have 584 people who liked US Football. Out of these, 181 liked football and soccer, and 77 liked football and Lacrosse. So, the remaining number of people who liked only football is 584 - 181 - 77 = 226.<br />- In the middle circle, we have 639 people who liked soccer. Out of these, 181 liked football and soccer, and 217 liked soccer and Lacrosse. So, the remaining number of people who liked only soccer is 639 - 181 - 217 = 241.<br />- In the right circle, we have 523 people who liked Lacrosse. Out of these, 217 liked soccer and Lacrosse, and 77 liked football and Lacrosse. So, the remaining number of people who liked only Lacrosse is 523 - 217 - 77 = 229.<br /><br />Now that we have filled in the Venn diagram, we can answer the questions:<br /><br />1. How many people liked only one sport?<br />To find the number of people who liked only one sport, we need to add the number of people who liked only football, only soccer, and only Lacrosse. So, the total number of people who liked only one sport is 226 + 241 + 229 = 696.<br /><br />2. How many people liked at least two sports?<br />To find the number of people who liked at least two sports, we need to add the number of people who liked football and soccer, football and Lacrosse, soccer and Lacrosse, and all three sports. So, the total number of people who liked at least two sports is 181 + 77 + 217 + 243 = 718.<br /><br />3. How many people liked none of the sports?<br />To find the number of people who liked none of the sports, we need to subtract the total number of people who liked at least one sport from the total number of people surveyed. So, the total number of people who liked none of the sports is 1472 - (226 + 241 + 229 + 181 + 77 + 217 + 243) = 1472 - 1473 = -1.<br /><br />Therefore, the answers to the questions are:<br />1. 696 people liked only one sport.<br />2. 718 people liked at least two sports.<br />3. -1 person liked none of the sports.