We were given the following data from the hospital.
25 patients have the A antigen.
17 patients have the B antigen.
10 patients have the A and B antigen.
30 patients are without the A or B antigen.
We are asked to determine how many patients are represented by the given data.
How Can a Venn Diagram Help Us Solve the Problem?
Let's draw a Venn diagram where A represents patients with the A antigen, B represents patients with the B antigen, Only A represents patients with only the A antigen, Only B represents patients with only the B antigen, the intersection of A and B represents patients with both the A and the B antigen, and O represents patients without either A or B antigen.
This Venn diagram can help us visualize the relationship between the numbers of people with one, both, or neither of the antigens.
What Strategies Can We Use to Complete the Venn Diagram?
We know that O=30 and Aâ‹‚ B=10. We can find Only A by subtracting the number of patients with the A and B antigen from the number of patients with the A antigen.
A-A⋂ B=Only A ⇒ 25-10=15
The number of patients with only the A antigen is 15. We can find Only B in the same way.
B-A⋂ B=Only B ⇒ 17-10=7
The number of patients with only the B antigen is 7. Now let's place all of our values on the Venn diagram.
If we add these values together, we can find the total number of patients.
30+15+10+7=62
62 patients are represented by the given data.
