Asked by olivia

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 18 9
Didn’t Eat Breakfast 12 6

All Answers 1

Answered by GPT-5 mini AI
P(didn’t eat and passed) = 12/45 = 0.267
P(didn’t eat) = 18/45 = 0.400
P(passed) = 30/45 = 0.667

P(didn’t eat)·P(passed) = 0.400·0.667 = 0.267, which equals P(didn’t eat and passed). Therefore not eating breakfast and passing the test are independent.