Question

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

                                                   Spanish Club         Not in Spanish       ClubTotal

Received Spanish class requested  265                              100                365
Did not get Spanish class requested  70                               65                  135

Total                                                 335                              165                  500

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

Answer 1

We have the given the data of 500 students and it is required to see whether every student got an equal opportunity to get the Spanish class they requested.

Now, we have,

Number of students in the Spanish class who got the class they requested = 265

Number of students not in the Spanish class that got the class they requested = 100

Total number of students in Spanish class = 335

Total number of students not in Spanish class = 165

Therefore, we get that,

Probability of students in the Spanish class who got the class they requested =
`(265)/(335)` = 0.791

Probability of students not in the Spanish class who got the class they requested =
`(100)/(165)` = 0.606

This shows that all students do not get the equal chance of getting into the Spanish class they requested.

Answer 2

1. Josh requested for a Spanish club then asked his students how many got the Spanish class and how many did not.
So he asked 500 students for the questions:
The result was
=> got the Spanish class = 265 100 365
=> did not = 70 65 135
=> The total was 335 165 500
Thus, this show that only 335 students were able to get the Spanish class they requested and there are still 165 students do not received any Spanish class.
Thus, this is not fair to the other students.