# Uncovering class labels based on conditional or prior class probability

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?

1. All samples have the same value for attribute X.
2. 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.).

• I do not have much inspiration for the title. Feel free to update with a more informative one. Is it possible to get a proper link to your lectures? – chl Sep 25 '12 at 15:07
• Has the course covered "information theory" by any chance? Entropy, mutual information, etc? – Michael McGowan Sep 25 '12 at 16:43
• Chl: The lectures are only accessible to the students of that univ. The course has not yet covered entropy or mutual information. We have studied decision tree, lift charts, ROC curves, Naïve Bayes ,quadratic loss, information loss but only theoritically. I think this question probably is based on what we have studied so far. – Jenn Sep 25 '12 at 17:05
• Jenn, FYI if you address chl by using the @ symbol (like this: @chl), he'll receive a notification that you responded to him. – Michael McGowan Sep 25 '12 at 17:11
• Thanks, Jenn. I have deleted your previous comment (for obvious reason of copyright). – chl Sep 25 '12 at 19:13