Answer
$0.4625$
Work Step by Step
Define the events
$A_{1}$ = "Belle Meade was called."
$A_{2}$ = "Oak Hill was called.."
$A_{3}$ = "Antioch was called."
$B$ = "A donation is achieved."
Compute the probability of calling each suburb, having a total of $4000$ phone numbers:
$P(A_{1})=\displaystyle \frac{1000}{4000}=0.25$
$P(A_{2})=\displaystyle \frac{1000}{4000}=0.25$
$P(A_{3})=\displaystyle \frac{2000}{4000}=0.5$
We are given by the text:
$P(B|A_{1})=0.60,$
$P(B|A_{2})=0.55,$
$P(B|A_{3})=0.35$
We can now apply the theorem
$$\begin{align*}
P(B)&=\displaystyle \sum_{i=1}^{n}P(B|A_{i})P(A_{i}) & & \\
&= 0.60\cdot 0.25+0.55\cdot 0.25+0.35\cdot 0.5 \\
& =0.4625 \end{align*}$$
