Question

Janet 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 4 2 8 Grade 10 7 11 8 Grade 11 14 15 9 Grade 12 11 5 10 Compare P(Grade 9 | opposed) with P(opposed | Grade 9).

Answer 1

Grade       In Favor     Opposed     Undecided          Total
9                 4                   2                    8                   14
10               7                  11                   8                    26
11               14                 15                  9                    38
12               11                 5                    10                  26
Total           36                 33                   35                 104

Above is a partial sum chart that will help us in our quest.

P(Grade 9 | opposed)
The probability of Grade 9, given opposed, is the portion of opposed students that are in grade 9. 
Total number opposed: 33
Number opposed in Grade 9: 2
P(Grade 9 | opposed) = 2 / 33 = 0.06

P(opposed | Grade 9)
Total Number Grade 9: 14
Number opposed in Grade 9: 2
P(opposed | Grade 9) = 2 / 14 = 0.14

Answer 2

Answer:

P(Grade 9 | opposed) < P(opposed | Grade 9)