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A group of students was surveyed to find out if they like fiction books and/or non-fiction books. The results of the survey are shown below:

- 44 students like fiction books.
- 8 students like fiction books but do not like non-fiction books.
- 51 students like non-fiction books.
- 5 students do not like fiction books or non-fiction books.

Four students created the tables below to represent the data. F represents fiction books, and NF represents non-fiction books.

\begin{tabular}{|r|l|l|l|}
\hline \multicolumn{4}{|c|}{ Jake } \\
\hline & Like F & Do Not Like F & Total \\
\hline Like NF & 36 & 15 & 51 \\
\hline Do Not Like NF & 8 & 5 & 13 \\
\hline Total & 44 & 20 & 64 \\
\hline
\end{tabular}

\begin{tabular}{|c|l|l|l|}
\hline \multicolumn{4}{|c|}{ Bella } \\
\hline & Like F & Do Not Like F & Total \\
\hline Like NF & 8 & 23 & 31 \\
\hline Do Not Like NF & 36 & 15 & 51 \\
\hline Total & 44 & 28 & 64 \\
\hline
\end{tabular}

\begin{tabular}{|r|l|l|l|}
\hline \multicolumn{4}{|c|}{ Cate } \\
\hline & Like F & Do Not Like F & Total \\
\hline Like NF & 23 & 8 & 31 \\
\hline Do Not Like NF & 15 & 36 & 51 \\
\hline Total & 38 & 44 & 82 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{ Rob } \\
\hline & Like F & Do Not Like F & Total \\
\hline Like NF & 36 & 15 & 51 \\
\hline Do Not Like NF & 8 & 5 & 13 \\
\hline Total & 44 & 20 & 64 \\
\hline
\end{tabular}

Which student's table is correct?

A. Jake
B. Bella
C. Cate
D. Rob

Sagot :

GinnyAnsweridn
Sure, let's solve this problem step by step.

Let's first summarize the given data:
1. 44 students like fiction books.
2. 8 students like fiction books but do not like non-fiction books.
3. 51 students like non-fiction books.
4. 5 students do not like fiction books or non-fiction books.

We'll use this information to fill in the two-way table for each student and determine which one is correct.

### Step-by-Step Analysis

#### Step 1: Calculate the Students Who Like Both Fiction and Non-Fiction
Since 8 students like fiction but do not like non-fiction:
[tex]\[ \text{Students who like both} = \text{Students who like fiction} - \text{Students who like fiction only} \][/tex]
[tex]\[ \text{Students who like both} = 44 - 8 = 36 \][/tex]

#### Step 2: Construct the Table for Each Student

##### Jake's Table
| Like NF | Do Not Like NF | Total |
|---------------|----------------|-------|
| Like F | 36 | 8 | 44 |
| Do Not Like F | 15 | 5 | 20 |
| Total | 51 | 13 | 64 |

- Check the row totals:
- First row (Like NF): [tex]\(36 + 15 = 51\)[/tex]
- Second row (Do Not Like NF): [tex]\(8 + 5 = 13\)[/tex]
- Row totals are correct.

- Check the column totals:
- First column (Like F): [tex]\(36 + 8 = 44\)[/tex]
- Second column (Do Not Like F): [tex]\(15 + 5 = 20\)[/tex]
- Column totals seem incorrect as it should be 20 and not 13 as it should include non-fiction.

##### Bella's Table
| Like NF | Do Not Like NF | Total |
|---------------|----------------|-------|
| Like F | 8 | 36 | 44 |
| Do Not Like F | 23 | 15 | 38 |
| Total | 31 | 51 | 64 |

- Check the row totals:
- First row (Like F): [tex]\(8 + 36 = 44\)[/tex]
- Second row (Do Not Like F): [tex]\(23 + 15 = 38\)[/tex]
- Second row incorrect

##### Cate's Table
| Like NF | Do Not Like NF | Total |
|---------------|----------------|-------|
| Like F | 23 | 8 | 31 |
| Do Not Like F | 15 | 36 | 51 |
| Total | 38 | 44 | 82 |

The table total is incorrect.

##### Rob's Table
| Like NF | Do Not Like NF | Total |
|---------------|----------------|-------|
| Like F | 5 | 23 | 28 |
| Do Not Like F | 36 | 8 | 44 |
| Total | 41 | 31 | 72 |

The table totals is incorrect.

The only student who has the correct table according to the provided data is:
Jake
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