can you please help me ❤
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.
45 ate breakfast and passed 5 ate breakfast and failed 36 did NOT eat breakfast and passed 4 did NOT eat breakfast and failed
To determine whether eating breakfast and passing the test are independent, we need to compare the probability of passing the test for those who ate breakfast to the overall probability of passing the test.
The total number of students who passed the test is 45 + 36 = 81.
The total number of students who did not pass the test is 5 + 4 = 9.
The total number of students who ate breakfast is 45 + 5 = 50.
The total number of students who did not eat breakfast is 36 + 4 = 40.
The probability of passing the test for those who ate breakfast is 45/50 = 0.900
The overall probability of passing the test is 81/90 = 0.900
Since the probability of passing the test for those who ate breakfast is the same as the overall probability of passing the test, eating breakfast and passing the test are independent.