Questions: The following table shows the occurrence of words in a selection of 10 comments, and whether the comment expresses a positive sentiment. Positive Sentiment "acceptable" "love" "very" ------------------------------------------------- 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 Determine P(- "very"). Give your answer as a percentage to one decimal place but without the % symbol.

The following table shows the occurrence of words in a selection of 10 comments, and whether the comment expresses a positive sentiment.

Positive Sentiment "acceptable" "love" "very"
-------------------------------------------------
1 1 0 1
1 1 0 0
1 0 1 0
1 0 0 1
0 1 0 0
0 1 1 0
0 1 0 1
0 1 0 0
0 0 1 0
0 0 0 1

Determine P(- "very"). Give your answer as a percentage to one decimal place but without the % symbol.

Transcript text: 8 Formula 2 points The following table shows the occurrence of words in a selection of 10 comments, and whether the comment expresses a positive sentiment. \begin{tabular}{|c|c|c|c|} \hline Positive Sentiment & "acceptable" & "love" & "very" \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0 \\ \hline 1 & 0 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 \\ \hline 0 & 1 & 0 & 0 \\ \hline 0 & 1 & 1 & 0 \\ \hline 0 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 0 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline \end{tabular} Determine P(-| "very"). Give your answer as a percentage to one decimal place but without the \% symbol. Type your answer...

Solution

Solution Steps

Step 1: Define the Problem

We need to determine the conditional probability \( P(-| \text{"very"}) \), which represents the probability that a comment does not express a positive sentiment given that the word "very" is present.

Step 2: Analyze the Data

From the provided table, we can extract the following information:

Total number of comments with the word "very" present.
Number of comments with "very" that express a negative sentiment.

Step 3: Count Occurrences

We count the occurrences based on the data:

Total comments with "very" (where the fourth column is 1):
- There are 4 comments with "very" present.
Comments with "very" and negative sentiment (where the first column is 0 and the fourth column is 1):
- There are 2 comments that have "very" and do not express a positive sentiment.

Step 4: Calculate the Conditional Probability

Using the counts from Step 3, we can calculate \( P(-| \text{"very"}) \):

\[ P(-| \text{"very"}) = \frac{\text{Number of comments with "very" and negative sentiment}}{\text{Total number of comments with "very"}} = \frac{2}{4} = 0.5 \]

Step 5: Convert to Percentage

To express this probability as a percentage:

\[ P(-| \text{"very"}) = 0.5 \times 100 = 50.0\% \]