Blood tests of 100 people showed that 53 had the antigen and 42 had the antigen. Another 29 had neither antigen and so are of type . How many people are of
type AB, having both the and antigens? Draw and label a Venn diagram that shows the number of people with blood types , and .
How many people are of type , having both the and antigens?
.

To determine the number of people with blood type AB, we’ll first establish the total population and sum of the known groups:

First, we find the number of people with at least one of the antigens (A or B):

So, 71 people have at least one of the antigens.

Now, according to the principle of inclusion-exclusion, we have:

Substituting in the values we have:

Now, we can solve for AB:

So, there are 24 people of type AB.

For the Venn diagram, label two overlapping circles: one for people with the A antigen, and the other for those with the B antigen. Inside the overlapping area (AB), write 24. In the A circle but not overlapping, write (A only), and in the B circle but not overlapping, write (B only). Outside these circles but within the total circle of 100, write 29 for type O.

In summary: