Example 3.30 from Statistics, 3.5 Tree and Venn Diagrams

Tree and Venn Diagrams: example 3.30

A person with type O blood and a negative Rh factor (Rh–) can donate blood to any person with any blood type. Four percent of African Americans have type O blood and a negative Rh factor, 5−10 percent of African Americans have the Rh– factor, and 51 percent have type O blood.

This is an empty Venn diagram showing two overlapping circles. The left circle is labeled O and the right circle is labeled RH-.

Figure 3.18

The “O” circle represents the African Americans with type O blood. The “Rh––" oval represents the African Americans with the Rh– –factor.

We will use the average of 5 percent and 10 percent, 7.5 percent, as the percentage of African Americans who have the Rh–– factor. Let O = African American with Type O blood and R = African American with Rh– –factor.

P(O) = ___________
P(R) = ___________
P(O AND R) = ___________
P(O OR R) = ____________
In the Venn Diagram, describe the overlapping area using a complete sentence.
In the Venn Diagram, describe the area in the rectangle but outside both the circle and the oval using a complete sentence.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
a. P(O) = .51

b. P(R) = .075 because an average of 7.5 percent of African Americans have the Rh– –factor.

c. P(O AND R) = 0.04 because 4 percent of African Americans have both Type O blood and the Rh– –factor.

d. P(O OR R) = P(O) + P(R) - P(O AND R) = .51 + .075 − .04 = .545

e. The area represents the African Americans that have type O blood and the Rh–– factor.
f. The area represents the African Americans that have neither type O blood nor the Rh–– factor.

How did it go?

Solution

Solution