Chapter 11.8, Problem 23E

a.

To determine

TO-DETERMINE the probability of blood type from a randomly selected resident.

Answer to Problem 23E

The probability that blood from a randomly selected resident will be either type A or type O is $\text{P}\left(\text{A or O}\right)=85\%$ .

Explanation of Solution

Given:

Consider the resident with type A blood be $\text{P}\left(\text{A}\right)=40\%$ and residents with type O blood be $\text{P}\left(\text{O}\right)=45\%$ .

  

Calculation:

The events are disjoint because one person can have only one type of blood.

  $\begin{array}{l}\text{P}\left(\text{A or O}\right)=\text{P}\left(\text{A}\right)\text{+P}\left(\text{O}\right)\left[\text{Probability of disjoint events}\right]\\ \text{P}\left(\text{A or O}\right)=40\%+45\%\left[\text{substitute probabilities}\right]\\ \text{P}\left(\text{A or O}\right)=85\%\left[\text{add}\right]\end{array}$

Hence, The probability that blood from a randomly selected resident will be either type A or type O is $\text{P}\left(\text{A or O}\right)=85\%$ .

b.

To determine

TO-DETERMINE the probability of blood type from a randomly selected resident.

Answer to Problem 23E

The probability that blood from a randomly selected resident will be either type B or type O is $\text{P}\left(\text{B or O}\right)=56\%$ .

Explanation of Solution

Given:

Consider the resident with type B blood be $\text{P}\left(\text{B}\right)=11\%$ and residents with type O blood be $\text{P}\left(\text{O}\right)=45\%$ .

  

Calculation:

The events are disjoint because one person can have only one type of blood.

  $\begin{array}{l}\text{P}\left(\text{B or O}\right)=\text{P}\left(\text{B}\right)+\text{P}\left(\text{O}\right)\left[\text{Probability of disjoint events}\right]\\ \text{P}\left(\text{B or O}\right)=11\%+45\%\left[\text{Substitute the probabilities}\right]\\ \text{P}\left(\text{B or O}\right)=56\%\left[\text{Add}\right]\end{array}$

Hence, The probability that blood from a randomly selected resident will be either type B or type O is $\text{P}\left(\text{B or O}\right)=56\%$ .