A survey was conducted asking 600 people their favorite genre of book. The table shows the number of people who preferred four possible genres: Adventure, Comedy, Mystery, and Romance. Part a asks how many people surveyed responded with a genre that is not listed in the table. Part b asks to find the probabilities of each genre response, including "other genre" and complete a probability model.

1. Problem Description

A survey was conducted asking 600 people their favorite genre of book. The table shows the number of people who preferred four possible genres: Adventure, Comedy, Mystery, and Romance. Part a asks how many people surveyed responded with a genre that is not listed in the table. Part b asks to find the probabilities of each genre response, including "other genre" and complete a probability model.

2. Solution Steps

a. First, we need to find the total number of people who preferred the genres listed in the table.

$TotalListed = Adventure + Comedy + Mystery + Romance$

$TotalListed = 90 + 102 + 150 + 132 = 474$

Next, we subtract the number of people who preferred the genres listed from the total number of people surveyed to find the number of people who preferred a genre not listed.

$Other = TotalSurveyed - TotalListed$

$Other = 600 - 474 = 126$

b. To find the probability of each genre, we divide the number of people who preferred that genre by the total number of people surveyed.

$P(Adventure) = \frac{90}{600} = \frac{3}{20} = 0.15$

$P(Comedy) = \frac{102}{600} = \frac{17}{100} = 0.17$

$P(Mystery) = \frac{150}{600} = \frac{1}{4} = 0.25$

$P(Romance) = \frac{132}{600} = \frac{11}{50} = 0.22$

$P(Other) = \frac{126}{600} = \frac{21}{100} = 0.21$

3. Final Answer

a. 126 people surveyed responded with a genre that is not listed in the table.

b.

P(Adventure) = 0.15

P(Comedy) = 0.17

P(Mystery) = 0.25

P(Romance) = 0.22

P(Other) = 0.21