Consider the following hypothetical case of ‘Drinking Water’ planning........ Yo
ID: 3126568 • Letter: C
Question
Consider the following hypothetical case of ‘Drinking Water’ planning........ You are the new Emergency Preparedness Planner for the city of Endeavor, NY. The utility lines and transformers in your city are old and in need of significant repairs. The city owns the aging power company and has insufficient tax revenue for repairs. Drinking water access becomes a serious issue when there are major power outages of three days - which happen at least twice per year. The city of Endeavor provides residents with free drinking water during these major power outages.
After several past planning fiascoes under the guidance of your math-averse predecessor, you initiate more statistically imaginative methodologies to estimate the increasing need for bottled drinking water during an extended power outage (typically 3 days long). In the past, your city has either had way too much on hand (waste of taxpayer dollars) or not nearly enough (taxpayer angst for not being prepared). Not everyone will accept the water for a variety of reasons.
The city provides you with considerable data on water demand collected during past power outages. After an examination of historical records, you determine the following percentage of households who will accept (A) or reject (R) an offer for bottled water on successive days of an outage. You notice that the probabilities change with each day and the trend is not surprising.
Power Accept Reject
Outage water water
Day1 25% 75%
Day2 40% 60%
Day3 80% 20%
To help you decide how much water to keep on hand you construct a tree diagram. This details the past history of decision probabilities; how many families will accept water, and how often.
Build a Tree Diagram analyzing this scenario. Afterwards use the diagram to give the probability as a percentage to answer the following questions:
1) Households accepting water every day.
2) Households accepting water exactly twice.
3) Households accepting water at least twice.
4) Households that never change their behavior
Explanation / Answer
Making the tree diagram in form of a table, the outcome AAA represents households accepting water on day 1, day 2 and day3
Similarly AAR represents households accepting water on day 1, day 2 but rejecting it on day 3 etc.
(The numbers in brackets in values of columns 1,2 and 3 represents the probability of that decision
Probability of outcome is calculated by multiplying the different probabilities of dicision taken on 3 days. (Multiplicative rule used)
1) Probability that Households accepting water every day = P(AAA) = 0.08
2) Probability that Households accepting water exactly twice = P(AAR) + P(ARA) + P(RAA) = 0.02 +0.12 + 0.24 = 0.38
3) Probability that Households accepting water at least twice = Probability that Households accepting water exactly twice + Probability that Households accepting water thrice (i.e., every day) = 0.38 + 0.08 = 0.46
4) Probability that Households that never change their behavior = P(AAA) + P(RRR) = 0.08 +0.09 = 0.17
Day 1 Day 2 Day 3 Outcome Probability Accept (0.25) Accept (0.4) Accept (0.8) AAA 0.08 Accept (0.25) Accept (0.4) Reject (0.2) AAR 0.02 Accept (0.25) Reject (0.6) Accept (0.8) ARA 0.12 Accept (0.25) Reject (0.6) Reject (0.2) ARR 0.03 Reject (0.75) Accept (0.4) Accept (0.8) RAA 0.24 Reject (0.75) Accept (0.4) Reject (0.2) RAR 0.06 Reject (0.75) Reject (0.6) Accept (0.8) RRA 0.36 Reject (0.75) Reject (0.6) Reject (0.2) RRR 0.09Related Questions
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