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 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 63 11 Didn't Eat Breakfast 102 50
The total number of students who passed the test is 63 + 102 = 165.
The total number of students who ate breakfast is 63 + 11 = 74.
The probability of passing the test is 165/200 = 0.825.
The probability of eating breakfast is 74/200 = 0.370.
The probability of passing the test given that a student ate breakfast is 63/74 = 0.851.
The probability of passing the test, P(Passed), is 0.825.
The probability of eating breakfast, P(Eating Breakfast), is 0.370.
The probability of passing the test given that a student ate breakfast, P(Passed|Eating Breakfast), is 0.851.
Since P(Passed|Eating Breakfast) is not equal to P(Passed), eating breakfast and passing the test are dependent events.