Chapter 5.3, Problem 86E

To determine

To find: the percentage of her votes comes from black voters.

Answer to Problem 86E

The percentage of her votes comes from black voters is $62.07\%$ .

Explanation of Solution

Given:

The percentage of category of voters in a large city are 40% white voters, 40% black voters, and 20% Hispanic voters.

Concept used:

Definition condition probability: $P\left(A/B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$

Calculation:

According to the question, the tree diagram is:

  

From exercise-84,

  $\begin{array}{l}P\left(\text{Support}\right)=0.5800\\ P\left(\text{black}\cap \text{Support}\right)=0.3600\end{array}$

Definition conditional probability:

  $P\left(A/B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}$

Thus, it obtained:

  $\begin{array}{l}P\left(\text{black/Support}\right)=\frac{P\left(\text{black}\cap \text{Support}\right)}{P\left(\text{support}\right)}\\ =\frac{0.36}{0.58}=0.6207=62.07\%\end{array}$

Hence, the percentage of her votes comes from black voters is $62.07\%$ .