Mabel, a CEO, is trying to decide whether to implement a new strategy for her organization. She has considered various qualitative factors, and would like to complement these factors with an objective analysis that relies on probabilities and expected values.

Mabel has compiled the following information

If she does nothing, profits will remain where they are currently.

If she implements the strategy, and it is successful, profit will increase by $$80,000.$ If she implements the strategy, and it is a failure, profit will decrease by $$40,000.$

Mabel has determined that the strategy will either succeed or fail, and there is no $$in between.$$ She assesses the probability of fail as $60\%.$

Annie, a consultant, has offered her analysis of the scenario. Her analysis involves providing a rating of either "favorable" $($which signals success$)$ or a rating of "unfavorable" $($which signals failure$).$

Annie says: $$I$\text{'}$m pretty good at this stuff. In past similar instances, when success had occurred, I identified the scenario as $$favorable$80\%$ of the time.$$ Annie also says: $$In past similar instances, when failure had occurred, I identified the scenario as $$unfavorable$70\%$ of the time.$$