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.