Question

a survey is conducted to study pet ownership in different age groups. the two-way table is given below:

\

$$\begin{tabular}{|l|c|c|c|} \\hline & dog & cat & no pet \\\\ \\hline young adult & 17 & 17 & 15 \\\\ \\hline middle aged & 23 & 10 & 15 \\\\ \\hline senior citizen & 22 & 25 & 1 \\\\ \\hline \\end{tabular}$$

what is the probability that a randomly selected person from this survey owns a cat, given they are a young adult?

\\(p(\text{cat} \mid \text{young adult}) = ?\\%\\)

round your answer to the nearest whole percent.

Explanation:

Find the total number of young adults

$$ \text{Total Young Adults} = 17 + 17 + 15 = 49 $$

Find the number of young adults who own a cat

$$ \text{Young Adults with Cat} = 17 $$

Calculate the conditional probability as a percentage

$$ P(\text{Cat} \mid \text{Young Adult}) = \frac{17}{49} \approx 0.3469 \approx 35\% $$

Answer:

What is the probability that a randomly selected person from this survey owns a cat, given they are a young adult?

\(P(\text{Cat} \mid \text{Young Adult}) =\) <blank>35</blank>%