But a very simple one. Just to check I'm not getting it wrong. Suppose you have a very large enclosure with 100 animals. 70 of these animals are cats, 30 are dogs. There is enough food for all the animals, but you introduce a new type of food, to see whether either cats or dogs will show a preference for it. You place the new food in the enclosure, in the form of 100 equal pieces. Each animal can take at most one piece. All animals can see and smell the food and have free access to it, undisturbed by their peers or by the other species. After some time, you observe that 8 pieces are eaten by dogs, 2 by cats. Can we say the following? - assuming that past observations predict future observations, given that the next piece of food is eaten, the probability that it is a dog eating it is 8/10. - so given that another N pieces of food are eaten, N*8/10 will most probably be eaten by dogs, and N*2/10 by cats, resulting in 4:1 odds that the the additional N pieces of food are eaten by dogs rather than cats. - by Bayes theorem, given that an animal approaching the new food is a dog, the probability that it will eat a piece is (8/10) / (30/100) * P(E), where P(E) is the overall probability that a piece of food is eaten; and similarly, given that an animal approaching the new food is a cat, the probability that it will eat a piece is (2/10) / (70/100) * P(E). - so if one cat and one dog were presented with one piece of the new food, the odds it will be eaten by the dog rather than by the cat are (8/10) / (30/100) / [(2/10) / (70/100)] = 28:3. - we would get 1:1 odds only if each group on animals in the 'test' had eaten a number of pieces proportional to their representation in the population, i.e. in this example, 3 pieces by dogs and 7 pieces by cats. - or in other words, in our example dogs are disproportionately more drawn to the new food than cats are, with odds of about 9:1. Does it make sense? Thanks! L PS Please consider that this is just a thought experiment to check my understanding of a statistical theory, no need to point out zoological or ethological contradictions.