Question

Urban voters In the election described in Exercise 84, if the candidate’s predictions come true, what percent of her votes come from black voters? (Write this as a conditional probability and use the definition of conditional probability.)

Short answer

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

Step-by-step solution

Step 1. Given Information

In a major city, $40$percent of white voters, $40$ percent black voters, and $20\%$ Hispanic voters make up the voting population.

Step 2. Concept Used

Condition probability: $P(A/B)=P(A\cap B)/P\left(B\right)$

Step 3. Calculation

The tree diagram is shown below, according to the question:

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

conditional probability: $P(A/B)=P(A\cap B)/P\left(B\right)$

As a result, the following was obtained:

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

As a result, black voters account for $62.07\%$ of her ballots.