Question

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

\

$$\begin{tabular}{|l|c|c|c|} \\hline & cake & cookies & ice cream \\\\ \\hline south & 6 & 5 & 12 \\\\ \\hline midwest & 14 & 4 & 4 \\\\ \\hline north & 10 & 7 & 6 \\\\ \\hline \\end{tabular}$$

what is the probability that a randomly selected person from this surveys favorite dessert is cookies, given they are from the north?

\\ p(\text{cookies} \mid \text{north}) = \quad\\% \\

round your answer to the nearest whole percent.

Explanation:

Identify the given values from the table

Using the Two-Way Tables knowledge point

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Calculate the total number of people from the North

Using the Two-Way Tables knowledge point

$$ \text{Total North} = 10 + 7 + 6 = 23 $$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(\text{Cookies} \mid \text{North}) = \frac{\text{North and Cookies}}{\text{Total North}} = \frac{7}{23} $$

Convert the probability to a percentage

Using the Conditional Probability knowledge point

$$
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Answer:

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

\(P(\text{Cookies} \mid \text{North}) =\) <blank>30</blank>%