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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.

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    $\begingroup$ You should look at the conditional probability. You convert the joint in the table to the conditional by "normalizing" it - divide them by the marginal probability (which is the column sum $0.25$). Then you will obtain $0.4$ and $0.6$ for them, and then you judge whether it is a majority / safe to predict ... etc. $\endgroup$
    – BGM
    Commented Aug 7, 2018 at 5:48

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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.

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