Question

Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the math class you requested?" The results are shown in the table below:

Answer 1

Honor roll Not on honor roll Total
Received math class requested 215 125 340
Did not get math class requested 80 80 160
Total 295 205 500

Answer 2

Help Andrew determine if all students at his school have an equal opportunity to get the math class they requested. Show your work and explain your process for determining the fairness of the class assignment process.

Answer 3

OK. Similar process to last question. There are two events: A - making the honor roll, and B - getting the requested math class. From the info in the table, can you calculate P(A)?

Answer 4

80?

Answer 5

Not quite. There are 295 (215 + 80) on the honor roll and 500 students total. So the probability is 295/500. What do you get?

Answer 6

Hello?

Answer 7

0.59

Answer 8

Good.

Answer 9

Now, of the 295 that makethe honor roll, 215 of them get the math class they want. What's P(B)?

Answer 10

0.41

Answer 11

No. The probability is 215/295 as explained above. What do you get?

Answer 12

Oh okay i made a mistake. 0.72

Answer 13

Watch your rounding. I get 0.7288 which doesn't round to 0.72. What should it be?

Answer 14

I wasn't sure if i should round, 0.73

Answer 15

I think the rounding is OK. If we need extra decimal places, we'll find out later in the problem.

Answer 16

OK. So you've determined that if a student makes the honor roll, they have about a 73% chance of getting the math class they want.

Answer 17

Now, look at the students that don't make the honor roll. There's 205 of them and 125 get the math class they want. What's the probability?

Answer 18

0.61

Answer 19

Great. So the students who don't make the honor roll have a 61% chance of getting the math class they want. Should be able to answer the question: Do all students have an equal chance of getting the math class they want. If not, which group has a better chance?

Answer 20

Turns out our very first calculation wasn't needed to answer the question so it can be ignored.

Answer 21

They do not , and students who do not make honor roll?

Answer 22

I agree with the first part. Recall, students who make the honor roll have a 73% chance of getting the class they want while 61% of the students who don't make the honor roll get the class they want. Which group has a better chance?

Answer 23

Hello?

Answer 24

Oh i forgot about that, so students who make honor roll have the advantage

Answer 25

Right. Good job.

Answer 26

Thank you very much :)

Answer 27

You're welcome