Problem

A movie studio surveyed married couples about the types of movies they prefer.
In the survey, the husband and wife were each asked if they prefer action, comedy, or drama.
Here is a summary of the data the studio got after asking 75 couples.
\begin{tabular}{|c|c|c|}
\hline Husband & Wife & \begin{tabular}{c}
Number of \\
couples
\end{tabular} \\
\hline action & action & 7 \\
\hline action & comedy & 1,3 \\
\hline action & drama & 5 \\
\hline comedy & action & 9 \\
\hline comedy & comedy & 4 \\
\hline comedy & drama & 9 \\
\hline drama & action & 10 \\
\hline drama & comedy & 12 \\
\hline drama & drama & 6 \\
\hline
\end{tabular}

Suppose the movie studio will ask 100 more couples about their movie preferences.
How many of these 100 couples will have at most one spouse prefer drama movies? Use the data to make a prediction.

Answer

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Answer

So, the predicted number of couples out of the next 100 where at most one spouse prefers drama movies is \(\boxed{44}\).

Steps

Step 1 :A movie studio surveyed 75 married couples about the types of movies they prefer. In the survey, the husband and wife were each asked if they prefer action, comedy, or drama. The data collected is summarized in the table below.

Step 2 :\begin{tabular}{|c|c|c|} \n\hline Husband & Wife & \begin{tabular}{c} Number of \ couples \end{tabular} \ \hline action & action & 7 \ \hline action & comedy & 13 \ \hline action & drama & 5 \ \hline comedy & action & 9 \ \hline comedy & comedy & 4 \ \hline comedy & drama & 9 \ \hline drama & action & 10 \ \hline drama & comedy & 12 \ \hline drama & drama & 6 \ \hline \n\end{tabular}

Step 3 :We are asked to predict how many of the next 100 couples surveyed will have at most one spouse who prefers drama movies. To do this, we first need to calculate the proportion of couples in the current survey where at most one spouse prefers drama movies.

Step 4 :We can calculate this proportion by adding the number of couples where both prefer action, both prefer comedy, the husband prefers action and the wife prefers comedy, and the husband prefers comedy and the wife prefers action. This gives us \(7 + 4 + 13 + 9 = 33\) couples.

Step 5 :We then divide this number by the total number of couples surveyed to get the proportion. This gives us \(33 / 75 = 0.44\).

Step 6 :We can then use this proportion to predict the number of such couples in the next 100 couples surveyed. This gives us \(0.44 * 100 = 44\).

Step 7 :So, the predicted number of couples out of the next 100 where at most one spouse prefers drama movies is \(\boxed{44}\).

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