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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 Aug 7 '18 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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