Question

Constructing a Venn diagram with 2 sets to solve a word problem

Answer 1

Step-by-step explanation

From the statement, we know that:

• n(A) = # of participants with anxiety = 66,

,

• n(D) = # of participants with drowsiness = 85,

,

• n(A∩D) = # of participants with both anxiety and drowsiness = 47.

(a) The number of participants that had drowsiness but not anxiety is:

`n(D\text{ and not }A)=n(D)-(A∩D)=85-47=38.`

(b) The number of participants that had anxiety or drowsiness is:

`n(A\cup D)=n(A)+n(B)-n(A\cap B)=66+85-47=104.`Answer

• 38 participants

,

• 104 participants