SOLUTION: 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

Question 1012313: 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).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Given Table:

	In Favor	Opposed	Undecided
Grade 9	6	2	7
Grade 10	5	11	8
Grade 11	12	15	11
Grade 12	17	5	13

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Let's add on the totals

	In Favor	Opposed	Undecided	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

The row and column totals are found by adding up the values in each corresponding row or column. For example. The "15" in the first row of the column total (far right column) is found by adding up the values in the first row (6+2+7 = 15). The other totals are found the same way.
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Let's first compute P(Grade 11 | opposed)

P(Grade 11 | opposed) = (# in grade 11 AND who are opposed)/(# who are opposed)

P(Grade 11 | opposed) = 15/33

P(Grade 11 | opposed) = 5/11

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Now let's compute P(Opposed | Grade 11)

P(Opposed | Grade 11) = (# in grade 11 AND who are opposed)/(# who are in grade 11)

P(Opposed | Grade 11) = 15/38
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So the two expressions P(Grade 11 | opposed) and P(Opposed | Grade 11) are NOT the same value (5/11 is not equal to 15/38). This means that the two events being in grade 11 and being opposed are NOT independent. The two events are dependent.
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