Stuck on this one!!

Shelly believes the honor roll students at her school have an unfair advantage in being assigned to the math class they request. She asked 500 students at her 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:

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

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

Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.

So,

P(B given A) = 125/205 = 0.609756

which rounds to 0.61

This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.

The chances have gone down from 68% to 61% roughly.

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It appears that being on the honor roll does affect your chances of getting into the class you want.

Therefore, all students do not have the same equal opportunity.

We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.

MrRoyal MrRoyal · Answer 2 · 2022-03-18T15:00:14+01:00

All students do not have equal opportunity.

From the table, we have the following parameters:

205 people are on honor roll call
340 people got the math class requested
500 people were surveyed

The above means that:

The probability that a person is on honor roll call is:

p1 = 205/500

p1 = 0.41

The probability that a person got the math class requested

p2 = 340/500

p2 = 0.68

Both probabilities are not equal.

Hence, it is true that all students do not have equal opportunity.