The two-way frequency table represents data from a survey asking mall visitors whether they like seafood, meat, both, or neither.

\begin{tabular}{|c|c|c|c|}
\hline & Meat & Not Meat & Total \\
\hline Seafood & 16 & 31 & 47 \\
\hline Not Seafood & 20 & 5 & 25 \\
\hline Total & 36 & 36 & 72 \\
\hline
\end{tabular}

Which is the joint relative frequency for mall visitors who like seafood and meat?

A. [tex]$\frac{5}{72}$[/tex]
B. [tex]$\frac{16}{72}$[/tex]
C. [tex]$\frac{20}{72}$[/tex]



Answer :

To determine the joint relative frequency for mall visitors who like both seafood and meat, let's follow these steps:

1. Identify the total number of mall visitors who like both seafood and meat:
According to the provided two-way frequency table, there are 16 mall visitors who like both seafood and meat.

2. Find the total number of survey respondents:
The total number of survey respondents (mall visitors) is given in the bottom right cell of the table, which is 72.

3. Calculate the joint relative frequency:
The joint relative frequency is found by dividing the number of respondents who like both seafood and meat by the total number of survey respondents. Hence, we have:

[tex]\[ \text{Joint Relative Frequency} = \frac{\text{Number of visitors who like seafood and meat}}{\text{Total number of visitors}} \][/tex]
[tex]\[ \text{Joint Relative Frequency} = \frac{16}{72} \][/tex]

4. Simplify the fraction if needed:
In this case, [tex]\( \frac{16}{72} \)[/tex] simplifies to [tex]\( 0.2222222222222222 \)[/tex].

Therefore, the joint relative frequency for mall visitors who like both seafood and meat is [tex]\( \frac{16}{72} \)[/tex] which numerically equals 0.2222222222222222.

The correct answer is [tex]\( \frac{16}{72} \)[/tex].