Answer :
To determine the probability that a randomly selected person from the Midwest prefers cake, we will follow these steps:
1. Identify the total number of people surveyed from the Midwest: From the table, the total number of individuals from the Midwest is 34.
2. Identify the number of people from the Midwest who prefer cake: According to the table, 20 people from the Midwest prefer cake.
3. Calculate the probability that a person from the Midwest prefers cake: The probability can be found by dividing the number of Midwest individuals who prefer cake by the total number of Midwest individuals.
[tex]\[ P(\text{Cake} \mid \text{Midwest}) = \frac{\text{Number of people from Midwest who prefer cake}}{\text{Total number of people from Midwest}} \][/tex]
[tex]\[ P(\text{Cake} \mid \text{Midwest}) = \frac{20}{34} \approx 0.5882352941176471 \][/tex]
4. Convert the probability to a percentage: Multiply by 100 to convert the probability to a percentage.
[tex]\[ 0.5882352941176471 \times 100 \approx 58.82352941176471 \% \][/tex]
5. Round the percentage to the nearest whole number: The percentage rounded to the nearest whole number is 59%.
Thus, the probability that a randomly selected person from this survey's favorite dessert is cake, given they are from the Midwest, is:
[tex]\[ P(\text{Cake} \mid \text{Midwest}) \approx 59\% \][/tex]
1. Identify the total number of people surveyed from the Midwest: From the table, the total number of individuals from the Midwest is 34.
2. Identify the number of people from the Midwest who prefer cake: According to the table, 20 people from the Midwest prefer cake.
3. Calculate the probability that a person from the Midwest prefers cake: The probability can be found by dividing the number of Midwest individuals who prefer cake by the total number of Midwest individuals.
[tex]\[ P(\text{Cake} \mid \text{Midwest}) = \frac{\text{Number of people from Midwest who prefer cake}}{\text{Total number of people from Midwest}} \][/tex]
[tex]\[ P(\text{Cake} \mid \text{Midwest}) = \frac{20}{34} \approx 0.5882352941176471 \][/tex]
4. Convert the probability to a percentage: Multiply by 100 to convert the probability to a percentage.
[tex]\[ 0.5882352941176471 \times 100 \approx 58.82352941176471 \% \][/tex]
5. Round the percentage to the nearest whole number: The percentage rounded to the nearest whole number is 59%.
Thus, the probability that a randomly selected person from this survey's favorite dessert is cake, given they are from the Midwest, is:
[tex]\[ P(\text{Cake} \mid \text{Midwest}) \approx 59\% \][/tex]
