Fill in the missing values in the given table.
Identify the given probabilities.
- Probability of reading USA Today (\( P(A) \)) = 0.40
- Probability of reading New York Times (\( P(B) \)) = 0.25
- Probability of reading both papers (\( P(A \cap B) \)) = 0.05
Calculate the probability of reading USA Today but not New York Times.
\( P(A \cap B^c) = P(A) - P(A \cap B) = 0.40 - 0.05 = 0.35 \)
Calculate the probability of reading New York Times but not USA Today.
\( P(B \cap A^c) = P(B) - P(A \cap B) = 0.25 - 0.05 = 0.20 \)
Calculate the probability of not reading either paper.
\( P(A^c \cap B^c) = 1 - P(A \cup B) = 1 - (P(A) + P(B) - P(A \cap B)) = 1 - (0.40 + 0.25 - 0.05) = 0.40 \)
Fill in the table with the calculated values.
\[
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & \text{Reads NYT} & \begin{tabular}{c} \text{Does NOT} \\ \text{Read NYT} \end{tabular} & \text{Total} \\
\hline
\text{Reads USA Today} & 0.05 & 0.35 & 0.40 \\
\hline
\begin{tabular}{c} \text{Does NOT read} \\ \text{USA Today} \end{tabular} & 0.20 & 0.40 & 0.60 \\
\hline
\text{Total} & 0.25 & 0.75 & 1 \\
\hline
\end{tabular}
\]
The completed table is:
\[
\boxed{
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & \text{Reads NYT} & \begin{tabular}{c} \text{Does NOT} \\ \text{Read NYT} \end{tabular} & \text{Total} \\
\hline
\text{Reads USA Today} & 0.05 & 0.35 & 0.40 \\
\hline
\begin{tabular}{c} \text{Does NOT read} \\ \text{USA Today} \end{tabular} & 0.20 & 0.40 & 0.60 \\
\hline
\text{Total} & 0.25 & 0.75 & 1 \\
\hline
\end{tabular}
}
\]
The completed table is:
\[
\boxed{
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & \text{Reads NYT} & \begin{tabular}{c} \text{Does NOT} \\ \text{Read NYT} \end{tabular} & \text{Total} \\
\hline
\text{Reads USA Today} & 0.05 & 0.35 & 0.40 \\
\hline
\begin{tabular}{c} \text{Does NOT read} \\ \text{USA Today} \end{tabular} & 0.20 & 0.40 & 0.60 \\
\hline
\text{Total} & 0.25 & 0.75 & 1 \\
\hline
\end{tabular}
}
\]
Answered
