a survey is conducted to study the favorite dessert of individuals in different regions. the two - way table…

a survey is conducted to study the favorite dessert of individuals in different regions. the two - way table is given below:\n| | cake | cookies | ice cream | total |\n|--|--|--|--|--|\n| south | 8 | 9 | 16 | 33 |\n| midwest | 20 | 4 | 10 | 34 |\n| north | 18 | 11 | 4 | 33 |\n| total | 46 | 24 | 30 | 100 |\nwhat is the probability that a randomly selected person from this surveys favorite dessert is cake, given they are from the midwest?\np(cake | midwest) = ?%\nround your answer to the nearest whole percent.

a survey is conducted to study the favorite dessert of individuals in different regions. the two - way table is given below:\n| | cake | cookies | ice cream | total |\n|--|--|--|--|--|\n| south | 8 | 9 | 16 | 33 |\n| midwest | 20 | 4 | 10 | 34 |\n| north | 18 | 11 | 4 | 33 |\n| total | 46 | 24 | 30 | 100 |\nwhat is the probability that a randomly selected person from this surveys favorite dessert is cake, given they are from the midwest?\np(cake | midwest) = ?%\nround your answer to the nearest whole percent.

Answer

Explanation:

Step1: Identificar valores de la tabla

El número de personas del Midwest que prefieren el pastel es 20, y el total de personas del Midwest es 34.

Step2: Aplicar fórmula de probabilidad condicional

La fórmula para la probabilidad condicional $P(A|B)=\frac{P(A\cap B)}{P(B)}$. En el contexto de una tabla de contingencia, $P(\text{Cake}|\text{Midwest})=\frac{\text{Número de personas del Midwest que prefieren el pastel}}{\text{Total de personas del Midwest}}$. Entonces $P(\text{Cake}|\text{Midwest})=\frac{20}{34}$.

Step3: Convertir a porcentaje

$\frac{20}{34}\approx 0.5882$. Multiplicando por 100 para obtener el porcentaje: $0.5882\times100 = 58.82%$. Redondeando al entero más cercano, obtenemos 59%.

Answer:

59%