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 gender in the following table. Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.

Passed Failed
Male 17 6
Female 34 12

Since P(mail |fail)=________ and P(male)=______, the two results are_____ so the events are________

Answer 1

Explanation:

From the given information:

Passed Failed Total

Male 17 6 23

Female 34 12 46

Total 51 18 69

`P(male | fail) = (P(male \cap fail))/( P(fail))`

`P(male | fail) = ((6)/(69) )/((18)/(69))`

`P(male| fail) = (1)/(3)`

`P(male | fail) = 0.333`

`P(male) = (23)/(69)`

`P(male) = \frac {1}{3}`

`P(male) = 0.333`

The two results are equal:

So the events are dependent.