Chapter 3: Q.3.3 (page 208)

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, $5 - 10 %$ of African Americans have the Rh- factor, and $51 %$ have type O blood.
The $“ O ”$ circle represents the African Americans with type O blood. The “Rh-“ oval represents the African Americans with the Rh- factor.
We will take the average of $5 %$ and $10 %$ and use $7.5 %$ as the percent of African Americans who have the Rh factor.
Let $O =$ African American with Type O blood and R = African American with Rh- factor.
a. $P (O) =$ _____
b. $P (R) =$ _
c. $P (O A N D R) =$ _
d. $P (O O R R) =$ ______
e. In the Venn Diagram, describe the overlapping area using a complete sentence.
f. In the Venn Diagram, describe the area in the rectangle but outside both the circle and the oval using a complete sentence.

Short Answer

Expert verified

a. $P (O) = 0.51$

b. $P (R) = 0.075$

c. $P (O \cap R) = 0.04$

d. $P (O \cup R) = 0.585$

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.

Step by step solution

Given information

type O blood $= 51 %$

type negative Rh- factor $= 5 - 10 %$

African American Rh- factor $= 7.5 %$

Part (a) Step 1: Explanation

The probability of type O blood for Africa American,

$P (O) = \frac{51}{100} = 0.51$

Part (b) Step 1: Explanation

The probability of type negative Rh- blood for Africa Americans,

$P (R) = \frac{7.5}{100} = 0.075$

Part (c) Step 1: Explanation

The probability of type O blood AND type negative Rh- factor,

$P (O \cap R) = P (O) . P (R) P (O \cap R) = 0.51 \times 0.075 P (O \cap R) = 0.03825 \approx 0.04$

Part (d) Step 1: Explanation

The probability of type O blood OR type negative Rh- factor,

$P (O \cup R) = P (O) + P (R) - P (O \cap R) P (O \cup R) = 0.51 + 0.075 - 0.04 P (O \cup R) = 0.545$

Part (e) Step 1: Explanation

In the Venn Diagram, the overlapping area, that is, the intersection area of type O blood and type negative Rh- factor blood of Africa Americans are about 4%. The area represents the African Americans that have type O blood and the Rh- factor.

Part (f) Step 1: Explanation

The area of the rectangle represents the African Americans that have neither type O blood nor the Rh- factor. That is, 45% of the African Americans that have neither type O blood nor the Rh- factor.