The joint relative frequency that a person surveyed likes both classical music and pop music is 0.41.
The joint relative frequency that a person surveyed likes classical music and pop music can be found using the following steps:
Identify the relevant data: From the table, we need to focus on the people who answered "Yes" to both classical and pop music. This is represented by the value in the top left cell, which is 82.
Calculate the total number of people surveyed: This is represented by the sum of all the values in the table, which is 200.
Divide the number of people who like both types of music by the total number of people surveyed: This will give you the joint relative frequency.
Therefore, the joint relative frequency is:
Joint relative frequency = Number of people who like both / Total number of people surveyed
Joint relative frequency = 82 / 200
Joint relative frequency = 0.41
So, the joint relative frequency that a person surveyed likes classical music and pop music is 0.41.
Here's a table summarizing the steps:
Step Description Value
1 Identify relevant data 82
2 Calculate total number of people surveyed 200
3 Calculate joint relative frequency 82 / 200 = 0.41