According to a recent survey of first-year high school students, 28% chew gum daily. The students were also asked if they had recently gotten a cavity filled at the dentist. Of the 47% of first-year students who responded that they had a cavity recently filled, only 39% chewed gum daily.Is chewing gum independent of having a cavity filled recently?

For gum chewing and having a cavity filled recently to be independent, the probability of chewing gum should be the same whether or not a student had a cavity filled. Here, P(Gum) = 28%, but P(Gum|Cavity) = 39%, so the probabilities differ and the events are not independent. The correct choice is C: P(Gum) ≠ P(Gum|Cavity).

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