Chapter 10.3, Problem 23E

(a)

To determine

To find: the probability that a randomly selected person does not own either pet.

Answer to Problem 23E

Here, the probability that a randomly selected person does not own either pet is $\text{0}\text{.4381}$ .

Explanation of Solution

Given:

  

Calculation:

A two-way table is the frequency table that displays data collected from one source that belong to two different categories. One category of data is represented by rows and another category of data is represented by columns.

Use the information from the given Venn diagram to construct the two-way table. The table is as follows:

	Owns a dog	Do not own a dog	Total
Owns a cat	$36$	$25$	$61$
Do not own a cat	$57$	$92$	$149$
Total	$93$	$117$	$210$

Table $10.323E$ two-way table.

Table $10.3-23E$ shows the frequencies.

Divide the frequencies in each cell by the total number of people surveyed. This will yield into the conditional relative frequency. Assume, event $A$ denote the person does not own either pet. Thus, the probability that a randomly selected person does not own either pet is as follows:

  $\begin{array}{l}P\left(A\right)=\frac{92}{210}\\ \text{ =0}\text{.4381}\end{array}$

Therefore, the answer is : $\boxed{\text{0}\text{.4381}}$ .

Conclusion:

Hence, the probability that a randomly selected person does not own either pet is $\text{0}\text{.4381}$ .

(b)

To determine

To find: the probability that a randomly selected person who owns a dog also owns a cat.

Answer to Problem 23E

Here, the probability that a randomly selected person who owns a dog also owns a cat is $\text{0}\text{.3871}$ .

Explanation of Solution

Calculation:

Assume, event $C$ denote a randomly selected person who owns cat and event $D$ denote the event that selected person owns a dog.

The required probability is as follows:

  $\begin{array}{l}P\left(C|D\right)=\frac{P\left(CandD\right)}{P\left(D\right)}\\ \text{ =}\frac{36/210}{93/210}\\ \text{ =0}\text{.3871}\end{array}$

Therefore, the answer is : $\boxed{\text{0}\text{.3871}}$ .

Conclusion:

Hence, the probability that a randomly selected person who owns a dog also owns a cat is $\text{0}\text{.3871}$ .