To solve this problem, we can use the principle of inclusion-exclusion and create a Venn diagram.
Let's denote:
A: students who like tennis
B: students who like football
C: students who like baseball
According to the given information:
A = 29
B = 31
A ∩ B = 11
A ∩ C = 19
B ∩ C = 22
A ∩ B ∩ C = 4
None of the sports = 3
We want to find the number of students who like only tennis and football, which is equal to:
(A ∩ B) - (A ∩ B ∩ C)
(A ∩ B) = 11
(A ∩ B ∩ C) = 4
Therefore, the number of students who like only tennis and football is 11 - 4 = <<11-4=7>>7.
Similarly, we can find the number of students who like only tennis and baseball:
(A ∩ C) - (A ∩ B ∩ C) = 19 - 4 = <<19-4=15>>15.
And the number of students who like only baseball and football:
(B ∩ C) - (A ∩ B ∩ C) = 22 - 4 = <<22-4=18>>18.
Lastly, we want to find the number of students who like only tennis and football:
A - (A ∩ B) - (A ∩ C) + (A ∩ B ∩ C) = 29 - 11 - 19 + 4 = <<29-11-19+4=3>>3.
Therefore, the number of students who like only tennis and football is 3.
In a survey of students about favorite sports, the results include 29 who like tennis, 31 who like football, 11 who like tennis and football, 19 who like tennis and baseball, 22 who like football and baseball, 4 who like all three sports, and 3 who like 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? How many students like only tennis and football?
1 answer