Question
In a survey of students about favorite sports, the results include 23 who like tennis,30 who like football, 7 who like tennis and football,19 who like tennis and baseball, 22 who like football and baseball, 4 who like all three sports, and 7 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
Answers
GPT 3.5
Let's solve this using a Venn diagram.
First, let's fill in the number of students who like each sport: Tennis = 23, Football = 30, Baseball = unknown.
Next, let's fill in the overlapping regions: Tennis & Football = 7, Tennis & Baseball = 19, Football & Baseball = 22, All three = 4.
Lastly, let's fill in the students who like none of the sports = 7.
Now, let's find the number of students who like only each combination.
Number of students who like only Tennis and Football = Tennis & Football - All three = 7 - 4 = 3.
Number of students who like only Tennis and Baseball = Tennis & Baseball - All three = 19 - 4 = 15.
Number of students who like only Baseball and Football = Football & Baseball - All three = 22 - 4 = 18.
First, let's fill in the number of students who like each sport: Tennis = 23, Football = 30, Baseball = unknown.
Next, let's fill in the overlapping regions: Tennis & Football = 7, Tennis & Baseball = 19, Football & Baseball = 22, All three = 4.
Lastly, let's fill in the students who like none of the sports = 7.
Now, let's find the number of students who like only each combination.
Number of students who like only Tennis and Football = Tennis & Football - All three = 7 - 4 = 3.
Number of students who like only Tennis and Baseball = Tennis & Baseball - All three = 19 - 4 = 15.
Number of students who like only Baseball and Football = Football & Baseball - All three = 22 - 4 = 18.