Question $1$

A tech startup is developing a new mobile application. If the startup successfully launches the app, it will earn a $$50,000$ profit; if the launch is unsuccessful, the startup will lose $$35,000.$ In the past, similar apps have been successful $60\%$ of the time. At a cost of $$5,000,$ a market test

to assess the app$$s potential can be conducted. If the test result is favourable, there is a $80\%$ chance that the app will be successful. If the test result is unfavourable, there is only a $30\%$ chance that the app will be successful. There is a $60\%$ chance of a favourable test result and a $40\%$ chance of an unfavourable test result.

$($a$)$ Illustrate the problem using a decision tree

$(33$ marks$)$

$($b$)$ Describe what is the tech startup$$s optimal strategy

$(3$ marks$)$

$($c$)$ What are some of the key data factors, uncertainties, and decisions involved in the optimal decision strategy using Generative AI$?$ Critically evaluate the AI output covering three strengths and three weaknesses. Summarise your findings by creating a diagram.

$(15$ marks$)$

$($d$)$ Suppose that based on historical data, $60$ mobile apps that have been successfully launched had previously been test marketed; of these $60$ apps, $51$ had a favourable market test. Similarly, of $40$ apps that had a launch failure, $9$ had an unfavourable market test. Solve for the four probabilities: $(1)$ launch success given favourable market

test, $(2)$ launch failure given favourable market test, $(3)$ launch success given unfavourable market test, and $(4)$ launch failure given unfavourable market test.

$(26$ marks$)$