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 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 6767 33
Didn’t Eat Breakfast 1414 1717
Answer
Attempt 1 out of 2

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

Answer 1

First find totals:
- Passed = 67 + 14 = 81
- Total = 67 + 33 + 14 + 17 = 131

P(didn’t eat breakfast) = 31/131 ≈ 0.237
P(pass) = 81/131 ≈ 0.618
So P(didn’t eat breakfast) × P(pass) ≈ 0.237 × 0.618 = 0.146 (rounded)

P(didn’t eat breakfast and pass) = 14/131 ≈ 0.107

Answer

Since P(didn’t eat breakfast)×P(pass) = 0.146 and P(didn’t eat breakfast and pass) = 0.107, the two results are not equal so the events are not independent.