I need help ASAP! Can anyone please check my work? Alex believes the honor roll students at his school have an unfair advantage in being assigned to the science class they request. He asked 500 students at his school the following questions: "Are you on the honor roll?" and "Did you get the science class you requested?" The results are shown in the table below: Help Alex determine if all students at his school have an equal opportunity to get into the science class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.

Okay so my problem is my teacher marked this question wrong, but when I checked over it I couldn't seem to find what I did wrong. Can anyone see and explain what I did wrong? I put the table and my work for the question below

A = event the person got the class they wanted

B = event the person is on the honor roll

P(A) = (number who got the class they wanted)/(number total)

P(A) = 379/500

P(A) = 0.758

There's a 75.8% chance someone will get the class they want

Let's see if being on the honor roll changes the probability we just found

So we want to compute P(A | B). If it is equal to P(A), then being on the honor roll does not change P(A).

A and B = someone got the class they want and they're on the honor roll

P(A and B) = 64/500

P(A and B) = 0.128

P(B) = 144/500

P(B) = 0.288

P(A | B) = P(A and B)/P(B)

P(A | B) = 0.128/0.288

P(A | B) = 0.44 approximately

This is what you have shown in your steps. This means if we know the person is on the honor roll, then they have a 44% chance of getting the class they want.

Those on the honor roll are at a disadvantage to getting their requested class. Perhaps the thinking is that the honor roll students can handle harder or less popular teachers.

Regardless of motivations, being on the honor roll changes the probability of getting the class you want. So Alex is correct in thinking the honor roll students have a disadvantage. Everything would be fair if P(A | B) = P(A) showing that events A and B are independent. That is not the case here so the events are linked somehow.

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