Question

A telephone solicitor is responsible for canvassing three suburbs. In the past, 60% of the completed calls to Belle Meade have resulted in contributions, compared to 55% for Oak Hill and 35% for Antioch. Her list of tele- phone numbers includes one thousand households from Belle Meade, one thousand from Oak Hill, and two thou- sand from Antioch. Suppose that she picks a number at random from the list and places the call. What is the probability that she gets a donation?

Answer 1

0.4625 or 46.25%

Explanation:

The data for the percentage of contribution and the percentage of numbers from each suburb is presented in the table bellow:

`\begin{array}{ccc}&Contribution (C)&Number(N)\\Belle\ Mead&0.60&0.25\\Oak\ Hill&0.55&0.25\\Antioch&0.35&0.5\end{array}`

The probability that she gets a donation is given by the sum of the probabilities of getting a donation from each suburb weighed by their respective percentage of numbers of the list:

`P(C) = P(C_B)+P(C_O)+P(C_A)\\P(C) =0.6*0.25+0.55*0.25+0.35*0.5\\P(C) = 0.4625`

The probability that she gets a donation is 0.4625 or 46.25%.