SOLUTION: Jamey wanted to understand whether students at her school were in favor of an extended school day. She surveyed some students and displayed the results in the table below:
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Question 1012311: Jamey wanted to understand whether students at her school were in favor of an extended 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
If the principal randomly selects a student in grade 9 from this survey, what is the probability that the student is in favor of extending the school day?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Given Table:
| In Favor | Opposed | Undecided |
|---|
| Grade 9 | 5 | 3 | 9 |
|---|
| Grade 10 | 8 | 12 | 9 |
|---|
| Grade 11 | 15 | 16 | 10 |
|---|
| Grade 12 | 12 | 6 | 11 |
|---|
---------------------------------------------------------
Let's add on the totals (row totals and column totals). These values represent the sum along the rows or columns.
| In Favor | Opposed | Undecided | Total |
|---|
| Grade 9 | 5 | 3 | 9 | 17 |
|---|
| Grade 10 | 8 | 12 | 9 | 29 |
|---|
| Grade 11 | 15 | 16 | 10 | 41 |
|---|
| Grade 12 | 12 | 6 | 11 | 29 |
|---|
| Total | 40 | 37 | 39 | 116 |
|---|
---------------------------------------------------------
"If the principal randomly selects a student in grade 9 from this survey"
So we're just focusing on the "grade 9" row. There are 17 students in this grade. There are 5 who are in favor, so
P(In favor | grade 9) = (# who are in grade 9 AND in favor)/(# who are in grade 9)
P(In favor | grade 9) = 5/17
---------------------------------------------------------
As a fraction, the probability is 5/17
As a decimal, the probability is approximately 0.2941176 (used a calculator)
As a percentage, the probability is approximately 29.41176%
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