Question

A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by those who did or did not eat breakfast in the following table. Determine whether eating breakfast and failing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Passed Failed
Did Eat Breakfast 7373 33
Didn’t Eat Breakfast 9090 6363
Answer
Attempt 1 out of 2

Since P(did eat breakfast | fail) =
and P(did eat breakfast) =
, the two results are
so the events are
.

Answer 1

Since P(did eat breakfast | fail) = 33/6396 ≈ 0.005 and P(did eat breakfast) = 7406/22859 ≈ 0.324, the two results are not equal so the events are not independent.