Given a research with the following results:
Favorite vegetable is spinach for 30% of the participants, and carrots for 70% of the participants.
40% of the participants play the drums, 50% play the piano and the other participants don't play any musical instrument.
The following probabilities have been found:
$P(piano \cap spinach) = 0.15$,
$P (drums \cap spinach) = 0.12$,
$P(piano \cap carrots) = 0.35$,
$P(drums \cap carrots) = 0.35$.
What can you say about the connection between favorite vegetables and musical aptitude? What is the probability that someone plays the drums and the piano?
For the first question I found that only the variables "carrot as favorite vegetable" and "playing the drums" are dependent, but I don't know what else I can say about it. About the second question I'm not sure what to do.
One last question, what is the assumption that is being made in the Naive Bayes algorithm and what does it exactly mean?