Question

Use the table to answer the question.

Apple Preferences of Elementary, Middle, and High School Students
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
Determine if events A (a student likes apples) and B (a student is in middle school) are independent events based on the probabilities provided.

(1 point)
Responses

No; the events are dependent because P(A)=0.913
and P(A|B)=0.92
.
No; the events are dependent because cap p open paren cap A close paren is equal to 0 point 9 1 3 and cap p open paren cap A divides cap b close paren is equal to 0 point 9 2 .

Yes; the events are independent because P(A)=P(A∩B)=0.92
.
Yes; the events are independent because cap p open paren cap A close paren is equal to cap p open paren the intersection of cap A and cap b close paren is equal to 0 point 9 2 .

No; the events are dependent because P(A)=0.93
and P(A∩B)=0.91
.
No; the events are dependent because cap p open paren cap A close paren is equal to 0 point 9 3 and cap p open paren the intersection of cap A and cap b close paren is equal to 0 point 9 1 .

Yes; the events are independent because P(A)=P(A|B)=0.90
.

Answer 1

No; the events are dependent because P(A) = 274/300 = 0.913 and P(A|B) = 92/100 = 0.92, and P(A) ≠ P(A|B).