Challenge 277: Can Conundrum
Dr Reasoner’s housemate has removed the labels from four cans of soup as they wanted them for proof of purchase to get a special offer from the soup manufacturer.
Two of the cans involved contain tomato soup and two contain carrot soup, but without labels they cannot be told apart. Dr Reasoner’s housemate has put two cans on the top shelf of the kitchen cupboard and the other two on the bottom shelf, and claims that soups of the same flavour are on the same shelf, but is unclear as to where each flavour is.
Dr Reasoner opens one can from the top shelf (tomato) and one from the bottom shelf (carrot). Regrettably, from past experience, Dr Reasoner does not trust her housemate to have sorted the cans correctly.
Given that the first two cans were different what is the probability that the remaining cans had actually been placed with their matching can?