Plumber Bob does 40% of the plumbing jobs in a small town. 30% of the people in town are unhappy with their plumbers, but 50% of bob’s customers are unhappy with his work. If your neighbour is not ha

The probability that the neighbor's plumber is Bob can be calculated using Bayes' theorem. Let event A be the neighbor being unhappy with their plumber, and event B be the neighbor's plumber being Bob. P(B|A) = P(A|B) * P(B) / P(A) We know that P(B) = 0.4, as Bob does 40% of the plumbing jobs in town. We also know that P(A) = 0.3, as 30% of the people are unhappy with their plumbers. We need to find P(A|B), the probability that the neighbor is unhappy given that Bob is their plumber. We know that 50% of Bob's customers are unhappy with his work, so P(A|B) = 0.5. Plugging these values into the formula, we get: P(B|A) = 0.5 * 0.4 / 0.3 P(B|A) = 2/3 or 0.67 Therefore, if the neighbor is unhappy with their plumber, there is a 67% chance that the plumber is Bob.