Question

A group of students at a high school took a standardized test. The number ofstudents who passed or failed the exam is broken down by gender in thefollowing table. Determine whether gender and passing the test areindependent by filling out the blanks in the sentence below, rounding allprobabilities to the nearest thousandth.

Answer 1

1) Since this is a Conditional Probability, we can write out the following formula for that:

`P(pass|male)=\frac{P(pass\text{ }\cap\text{ male)}}{P(\text{male)}}`

2) Now, in the table we can see that the subspace for those who passed is the sum of all who passed:

28 +12 = 40

The Subspace for the students is:

21 +49 = 70

And now we can plug into that formula checking in the table:

`\begin{gathered} P(pass|male)=\frac{P(pass\text{ }\cap\text{ male)}}{P(\text{male)}} \\ P(pass|male)=((12)/(40))/((40)/(70))=(12)/(40)\cdot(40)/(70)=(6)/(35)\text{ or 0.17}1 \end{gathered}`

2.2) The Probability of being approved:

`P(\text{pass)}=(40)/(70)=(4)/(7)=0.571`

We can check whether two events are independent if we can state that