# Predicting based on probability table

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.

• 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.
– BGM
Commented Aug 7, 2018 at 5:48