Respuesta :
The Probability John Jenkins was interested in is obtained as [tex]0.75[/tex]
Probability:
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
The probability formula can be expressed as P (B) is the probability of an event 'B' n (B) is the number of favorable outcomes of an event 'B'.
Let the event,
S = Successive Driving Range
US = Unsuccessive Driving Range
FR = Favourable result from Research
UF = Unfavourable result from Research1.
Given that,John believes that the chance of a successful driving range is about 40%
[tex]P(S)=0.40[/tex]
By complementary probability[tex]P(US)=1-0.40=0.60[/tex]
Also, the probability that the research will be favorable if the driving range facility will be successful [tex]P\left ( FR\mid S \right )=0.90[/tex]
By complementary probability,[tex]P\left ( UF\mid S \right )=0.10[/tex] and Probability that the marketing research will be unfavorable if indeed the facility will be unsuccessful [tex]P\left ( UF\mid US \right )=0.80[/tex]
By complementary probability,
[tex]P\left ( FR\mid US \right )=0.20[/tex]
Need to find out chances of a successful driving range given a favorable result from the marketing survey i.e. [tex]P\left ( S\mid FR \right )[/tex]
By Bayes theorem,
[tex]P\left ( S\mid FR \right )=\frac{P\left ( FR\mid S \right )P\left ( S \right )}{P\left ( FR \right )} \\ =\frac{P\left ( FR\mid S \right )P\left ( S \right )}{P\left ( FR\mid S \right )P\left ( S \right )+P\left ( FR\mid US \right )P\left ( US \right )} \\ =\frac{\left (0.90 \right )\left ( 0.40 \right )}{\left ( 0.90 \right )\left ( 0.40 \right )+\left ( 0.20 \right )\left ( 0.60 \right )} \\ =0.75[/tex]
Therefore, the Probability John Jenkins was interested in is obtained as [tex]0.75[/tex]
Learn more about the topic Probability: https://brainly.com/question/26387628
