In: Statistics and Probability

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?

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.

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...

Driving Force is a golf ball manufacturer. Their R & D
department have been developing a type of golf ball with a new
dimpling pattern that is designed to increase the flight distance
of the ball. They are at the testing stage and run an experiment to
test the mean flight distance for the new type of ball compared to
a standard one. A special device is used to fire the balls at a set
force and angle.
A sample...

Driving Force is a
golf ball manufacturer. Their R & D department have been
developing a type of golf ball with a new dimpling pattern that is
designed to increase the flight distance of the ball. They are at
the testing stage and run an experiment to test the mean flight
distance for the new type of ball compared to a standard one. A
special device is used to fire the balls at a set force and
angle.
A sample...

Driving Force is a golf ball manufacturer. Their R & D
department have been developing a type of golf ball with a new
dimpling pattern that is designed to increase the flight distance
of the ball. They are at the testing stage and run an experiment to
test the mean flight distance for the new type of ball compared to
a standard one. A special device is used to fire the balls at a set
force and angle.
A sample...

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