##### 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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