Predicting based on probability table ![enter image description here]( I have a table above denoting the probabilities for certain criteria. Based on it, is it safe to assume that we could predict that a person liking rock music will lead to he/she liking heavy metal too? In my opinion, I would say no since liking rock music and not liking heavy metal has the probability of $0.1$ where as liking rock music and liking heavy metal has the probability of $0.15$. Since $0.1$ and $0.15 $is not too far off from each other in terms of value, i assume that we cannot predict that liking rock music will lead to he/she liking heavy metal. Would love some advice on whether my justification is right.

The quantity you are interested is P(M=1|R=1) i.e the probability that a person likes heavy metal given that they like rock music.

This is calculated as follows:

P(M=1|R=1)=P(M=1 and R=1)/P(R=1)= 0.15/(0.15+0.1) = 0.6

You can interpret this as: there is a 60% chance that someone who likes rock music will also like heavy metal music.