I dont understand how the lecturer solved this problem. The question is:
You are working with a dataset that contains descriptions of toxic and non-toxic substances. The dataset, which consists of 1000 samples from each of the two classes, is described in terms of a class label and a number of attributes. The dataset is sorted so that the 1000 toxic samples come first, followed by the 1000 non-toxic samples. Someone tells you that they have confirmed that, for this data set, the conditional probability that is gained from knowledge about attribute X is not different from the prior class probability. Assuming that they are correct, which of the following statements could be correct and which could not be correct?
- All samples have the same value for attribute X.
- All toxic samples have the same value for attribute X while each of the non-toxic samples has its own random value for attribute X.
My question is how can either of these answers to this question be correct when the information given is very limited?
The book we use for data mining is Witten and Frank, Data Mining: Practical Machine Learning Tools and Techniques, Morgan Kaufmann, 2011 (3rd ed.).