To determine if events A and B are independent, we need to calculate the probability of event A (liking apples) and event B (being in middle school) occurring simultaneously.
P(A and B) = P(A) * P(B)
P(A) = Total likes apples / Total students = 274/300 = 0.9133
P(B) = Total middle school students / Total students = 100/300 = 0.3333
P(A and B) = Middle school students who like apples / Total students = 92/300 = 0.3067
So, P(A and B) = 0.3067
Since P(A) * P(B) = 0.9133 * 0.3333 = 0.3044 ≠ P(A and B), events A and B are dependent.
Use the table to answer the question. Grade Level Apple Preference Elementary School Students Middle School Students High School Students Total Likes apples 85 92 97 274 Dislikes apples 15 8 3 26 Total 100 100 100 300 Let A be the event that a student likes apples. Let B be the event that a student is in middle school. Based on the data in the table, are events A and B independent?
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