To solve the problem of finding the probability that a randomly selected person who prefers ice cream is from the South, we need to follow these steps systematically:
1. Identify the total number of people who prefer ice cream:
According to the two-way table, the total number of people whose favorite dessert is ice cream is [tex]\( 30 \)[/tex].
2. Determine the number of people from the South whose favorite dessert is ice cream:
From the data in the table, the number of people from the South who prefer ice cream is [tex]\( 16 \)[/tex].
3. Calculate the conditional probability:
The conditional probability that a person is from the South given that their favorite dessert is ice cream is calculated by the ratio of the number of South people who prefer ice cream to the total number of ice cream lovers. Mathematically, this is represented as:
[tex]\[
P(\text{South | Ice Cream}) = \frac{\text{Number of South people who love ice cream}}{\text{Total number of people who love ice cream}}
\][/tex]
Plug in the numbers we have:
[tex]\[
P(\text{South | Ice Cream}) = \frac{16}{30}
\][/tex]
4. Convert the fraction to a percentage:
To get the probability in percentage form, we need to multiply the fraction by 100:
[tex]\[
P(\text{South | Ice Cream}) = \left( \frac{16}{30} \right) \times 100
\][/tex]
[tex]\[
P(\text{South | Ice Cream}) \approx 53.3333\%
\][/tex]
5. Round the result to the nearest whole percent:
Finally, we round [tex]\( 53.3333\% \)[/tex] to the nearest whole percent. This gives us:
[tex]\[
P(\text{South | Ice Cream}) \approx 53\%
\][/tex]
Therefore, the probability that a randomly selected person from this survey is from the South, given their favorite dessert is ice cream, is approximately 53%.
