Request for urgent Help in a Probability Question

Reply Thu 25 Nov, 2021 07:42 am
Dear Friends, I hope you are all fine, I am facing a serious issue in solving this question. Kindly guide me that how to solve this question.
I have written the answer to this question (part b and part c) but the answer is not clear. I just want to make two lists (1) List of Mutually exhaustive, (2) List of collectively exhaustive.

Question: Southern Bell is considering the distribution of funds for a campaign to increase long-distance calls within North Carolina. The following table lists the markets that the company considers worthy of focused promotions:
Market segments Cost of Special Campaign Aimed at Group
Minorities $350,000
Businesspeople $550,000
Women $250,000
Professionals and white-collar workers $200,000
Blue-collar workers $250,000

There is up to $800,000 available for these special campaigns.
(a) Are the market segments listed in the table collectively exhaustive? Are they mutually exclusive?
(b) Make a collectively exhaustive and mutually exclusive list of the possible events of the spending decision.
(c) Suppose the company has decided to spend the entire $800,000 on special campaigns.
Does this change your answer to part (b)? If so, what is your new answer?

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Part (a): The segments are collectively exhaustive because we can select any segments for special campaigns. There are two senses of mutually exclusive, (1) If we consider all possible combinations, then it is mutually exclusive. Let's consider only those combinations that fall in the range of our total amount ($ 800,000). They are not mutually exclusive because we want to consider Minorities and Businesspeople ($350,000+$550,000=$900,000), which is not possible simultaneously and exceeds the total available amount (800,000).

The answer of Part (b): We are supposing that Minorities=M; Business people=BP; Women=W; Professionals and white-collar workers =PWW; Blue-collar workers=BCW

M= $350,000;
BP= $550,000;
W= $250,000;
PWW= $200,000;
BCW= $250,000;
(M,W)=M= $350,000+ W= $250,000=$600,000;
(M,PWW)=M= $350,000+ PWW= $200,000=$530,000;
(M,BCW)=M= $350,000+ BCW= $250,000=$600,000;
(BP,W)= BP= $550,000+ W= $250,000=$800,000;
(BP,PWW)= BP= $550,000+ PWW= $200,000=$750,000;
(BP,BCW)= BP= $550,000+ BCW= $250,000=$800,000;
(W,PWW)= W= $250,000+ PWW= $200,000=$450,000;
(W,BCW)= W= $250,000+ BCW= $250,000=$500,000;
(PWW,BCW)= PWW= $200,000+ BCW= $250,000=$450,000;
(M,W, BCW)= M= $350,000+ W= $250,000+ BCW= $250,000=$850,000
(M,PWW, BCW)= M= $350,000+ PWWW= $200,000+ BCW= $250,000=$800,000
(W,PWW, BCW)= M= $250,000+ W= $200,000+ BCW= $250,000=$750,000
List of Mutually exhaustive:?
List of collectively exhaustive:?

Answer of Part (C):
(BP,W)= BP= $550,000+ W= $250,000=$800,000;
(BP,BCW)= BP= $550,000+ BCW= $250,000=$800,000;
(M,W, BCW)= M= $350,000+ W= $250,000+ BCW= $250,000=$850,000
(M,PWW, BCW)= M= $350,000+ PWWW= $200,000+ BCW= $250,000=$800,000

List of collectively exhaustive:?
List of Mutually exhaustive:?
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