According to a recent survey of first-year high school students, 28 percent chew gum daily. The students were also asked if they had recently gotten a cavity filled at the dentist. Of the 47 percent of first-year students who responded that they had a cavity recently filled, only 39 percent chewed gum daily. Is chewing gum independent of having a cavity filled recently?
Answer
A
Yes, cap p times Gum is equal to cap p times open paren Gum divides Cavity close paren .
B
No, cap p times Gum is not equal to cap p times open paren Gum divides Cavity close paren .
C
No, cap p times Gum is not equal to cap p times open paren Cavity divides Gum close paren .
D
Yes, cap p times Gum is equal to cap p times open paren Cavity divides Gum close paren .
Explanation
For gum chewing and recently having a cavity filled to be independent, the probability of chewing gum should be the same overall as it is among students who recently had a cavity filled. Those probabilities are 28% and 39%, respectively, so they are not equal; the events are not independent. Choice B states this comparison.
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