Question

In: Statistics and Probability

Developing a small driving range for golfers of all abilities has long been a desire of...

Developing a small driving range for golfers of all abilities has long been a desire of Kadio. Kadio, however, believes that the chance of a successful driving range is only about 40%. A friend of Kadio’s has suggested that he conduct a survey in the community to get a better feeling of the demand for such a facility. There is a 0.9 probability that the research will be favorable if the driving range facility will be successful. Furthermore, it is estimated that there is a 0.8 probability that the marketing research will be unfavorable if indeed the facility will be unsuccessful. Kadio would like to determine the chances of a successful driving range given a favorable result from the marketing survey.
1. Draw the a priori diagram tree.
2. Draw the a posteriori diagram and fill the branches with all needed probabilities.
Unexplained results will receive no credit.
3. What is the probability Kadio was interested in?

Solutions

Expert Solution

Let the event S = Successive Driving Range US = Unsuccessive Driving Range FR = Favourable result from Research UF = Unfavourable result from Research

1. A priori tree diagram:

2. Posteriori diagram:

3. Given:

Kadio, believes that the chance of a successful driving range is about 40% P(S) = 0.40; By complementary probability, P(US) = 1 - 0.40 = 0.60 Also,Probability that the research will be favorable if the driving range facility will be successful P(FR|S) = 0.90, By complementary probability, P(UF|S) = 0.10 and Probability that the marketing research will be unfavorable if indeed the facility will be unsuccessful P(UF|US) = 0.80, By complementary probability, P(FR|US) = 0.20

To find: Chances of a successful driving range given a favorable result from the marketing survey i.e. = ?

By Bayes theorem,

  

  

= 0.75

Hence, the probability Kadio was interested in is obtained as 0.75.


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