A survey is conducted to study the favorite dessert of individuals in different regions. The two-way table is given below:

\begin{tabular}{|l|c|c|c|c|}
\hline
& Cake & Cookies & Ice Cream & Total \\
\hline
South & 8 & 9 & 16 & 33 \\
\hline
Midwest & 20 & 4 & 10 & 34 \\
\hline
North & 18 & 11 & 4 & 33 \\
\hline
\multicolumn{1}{|c|}{ Total } & 46 & 24 & 30 & 100 \\
\hline
\end{tabular}

What is the probability that a randomly selected person from this survey's favorite dessert is cake, given they are from the Midwest?

[tex]$
P (\text{Cake} \mid \text{Midwest}) = [?] \%
$[/tex]

Round your answer to the nearest whole percent.



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]