Question

cats and dogs
a survey polls 34 participants and asks them how many dogs they have. they can respond with 0 dogs, 1 dog, or 2+ dogs. the survey similarly asks them how many cats they have. the results of the 34 responses are shown in the table below. note that many people have both dogs and cats.

	0 dogs	1 dog	2+
1 cat	5	3
2+ cats	3	3
total	9	13

2 multiple choice 1 point
if a participant is selected at random from this group, what is the probability that they own exactly 1 cat and exactly 1 dog?
27/34
24/34
3
3/13
3/34
3 fill in the blank 5 points
how many participants own exactly 1 cat? type your answer...
how many participants own exactly 1 dog? type your answer...
how many participants own exactly 1 cat and exactly 1 dog? type your answer...
referring to the union rule, how many participants own exactly 1 cat or exactly 1 dog?

Explanation:

Step1: Find number of participants with exactly 1 cat

Sum the values in the "1 cat" row: $5 + 3+3=11$.

Step2: Find number of participants with exactly 1 dog

Sum the values in the "1 dog" column: $7 + 3+3 = 13$.

Step3: Find number of participants with exactly 1 cat and 1 dog

From the table, the value at the intersection of "1 cat" row and "1 dog" column is 3.

Step4: Use the union - rule for number of participants with exactly 1 cat or 1 dog

The union rule is $n(A\cup B)=n(A)+n(B)-n(A\cap B)$. Here, $n(A) = 11$ (exactly 1 cat), $n(B)=13$ (exactly 1 dog), and $n(A\cap B) = 3$. So $n(A\cup B)=11 + 13-3=21$.

Step5: Calculate probability for question 2

The total number of participants is 34. The number of participants with exactly 1 cat and exactly 1 dog is 3. The probability $P=\frac{3}{34}$.

Answer:

1. E. $\frac{3}{34}$
2. How many participants own exactly 1 cat? 11

How many participants own exactly 1 dog? 13
How many participants own exactly 1 cat and exactly 1 dog? 3
Referring to the union - rule, how many participants own exactly 1 cat or exactly 1 dog? 21