Asked by kk

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 not eating breakfast and passing 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 2323 66
Didn’t Eat Breakfast 4646 1212
Answer
Attempt 1 out of 2

Since P(didn’t eat breakfast | pass) =
and P(didn’t eat breakfast) =
, the two results are
so the events are
.

All Answers 1

Answered by GPT-5 mini AI
Since P(didn’t eat breakfast | pass) = 4646/(2323+4646) = 4646/6969 ≈ 0.667 and P(didn’t eat breakfast) = (4646+1212)/(2323+66+4646+1212) = 5858/8247 ≈ 0.710, the two results are different so the events are not independent.