Question

Alex wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table below:

In favor Opposed Undecided
Grade 9 5 3 9
Grade 10 8 12 9
Grade 11 15 16 10
Grade 12 12 6 11
Compare P(Grade 12 | opposed) with P(opposed | Grade 12).

Answer 1

@astrid1

Answer 2

above is the chart and the answer options are:
P(Grade 12 | opposed) = P(opposed | Grade 12)

P(Grade 12 | opposed) > P(opposed | Grade 12)

P(Grade 12 | opposed) < P(opposed | Grade 12)

There is not enough information.

Answer 3

@joe348

Answer 4

Hi and welcome to QuestionCove!

P(Grade 12 | opposed) is the probability that the student is in grade 12, given that they oppose extending the school day. We can calculate this probability by taking ([Number of students in grade 12 AND oppose extending the school day]/[Number of students who oppose extending the school day])
The chart shows that 6 students are in grade 12 AND oppose extending the school day. The chart shows that 37 students total oppose extending the school day.
So, P(Grade 12 | opposed) = 6/37

P(opposed | Grade 12) is the probability that the student opposes extending the school day, given that they are in grade 12. We can calculate this probability by taking ([Number of students in grade 12 AND oppose extending the school day]/[Number of students who are in grade 12])
Like before, 6 students are in grade 12 AND oppose extending the school day. We also see that there are 29 total students in grade 12.
So, P(Grade 12 | opposed) = 6/29

Which of these two probabilities is greater?