Krissy 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 6 2 7 grade 10 5 11 8 grade 11 12 15 11 grade 12 17 5 13 compare p(grade 11 | opposed) with p(opposed | grade 11).

P(Grade 11 | opposed) =0.4545

P(opposed | Grade 11)=0.3947

Step-by-step explanation:

The table displaying the data is given below as:

                  In favorOpposedUndecided     Total

Grade 9          6                    2                  7                  15

Grade 10         5                   11                  8                  24

Grade 11          12                 15                  11                 38

Grade 12         17                  5                   13                 35

Total             40                 33                 39              112

Now we are asked to compare the conditional probability i.e. we are asked to compare  P(Grade 11 | opposed) with P(opposed | Grade 11).

let A denote the event that the student is in grade 11.

and B denote the event of opposing the decision.

Then A∩B denote the event of grade 11 students who opposed.

Hence, we are asked to compare:

P(A|B) and P(B|A)

We know that:

Now from the table we have:

P(A)=38/112

P(B)=33/112

P(A∩B)=15/112

Hence,

Similarly:

Hence,

P(Grade 11 | opposed) =0.4545

P(opposed | Grade 11)=0.3947

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent