A potential buyer is trying to decide if a new motorcycle is…

A potential buyer is trying to decide if a new motorcycle is good or bad. The prior belief that the motorcycle is good is 50%. Then the potential buyer receives signals (test rides), where g represents a good test ride performance and b represents a bad test ride performance by the motorcycle. Also good motorcycles perform well on test rides and bad motorcycles ride poorly on test rides with 60% probability. Given that the potential buyer goes on a single good test ride, followed by two bad test rides, what is her posterior probability that the motorcycle is a good one?

Sam lives for three periods: youth, middle age, and old age….

Sam lives for three periods: youth, middle age, and old age. In each period, he chooses whether to eat chocolate or not. Once Sam tries it, he becomes addicted in the next period and remains addicted forever. Assume that, in youth, Sam is not addicted to chocolate. Sam’s utility depends on the state of addiction: U ( eating chocolate | addicted ) = -4 U ( eating chocolate | not addicted ) = 4 U ( not eating chocolate | addicted ) = -10 U ( not eating chocolate | not addicted ) = 2 Assume delta = 0.5 (

True or False: The following scenario is an example of confi…

True or False: The following scenario is an example of confirmation bias. John hears a rumor that his co-worker Barry is having an affair with his co-worker Mary, but he is initially unsure that it is true. On Monday, John notices that Barry smiling at Mary when talking about their TPS reports. On Tuesday, John observes Mary holding eye-contact with Barry while discussing the situation with the loading dock. Finally, on Wednesday John sees Barry wink at Mary after telling her an anecdote that ended with him saying “I tried to enter the bare-knuckle boxing tournament this past weekend but for the life of me I couldn’t find anywhere to get bear knuckles.” At this point, John is certain that they were having an affair. 

In a certain city, 1% of the population has a rare medical c…

In a certain city, 1% of the population has a rare medical condition. A diagnostic test for this condition has an accuracy of 95%, meaning that it correctly identifies the condition in 95% of cases when it is present, and correctly identifies the absence of the condition in 75% of cases when it is not present. If a randomly selected individual from this city tests positive for the condition, what is the probability that they actually have the condition?