7. A survey asked 2082 adults if they owned a home. A total of 1249 survey respondents answered Yes. Of the 450 respondents in the $$ 18-34 $$ age groups, 117 responded Yes. Required: A. What is the probability that a respondent to the poll owned a home? B. What is the probability that a respondent in the $$ 18-34 $$ age group owned a home? C. What is the probability that a respondent to the poll did not own a home? D. What is the probability that a respondent in the $$ 18-34 $$ age group did not own a home?

Question

UpStudy AI · Accepted Answer

Let's analyze each part of the problem step by step.

### Given Data:
- **Total respondents:** 2,082
- **Total "Yes" responses (owned a home):** 1,249
- **Respondents in the 18-34 age group:** 450
- **"Yes" responses in the 18-34 age group:** 117

---

### **A. Probability that a respondent to the poll owned a home**

**Calculation:**
$$ \text{Probability} = \frac{\text{Number of "Yes" responses}}{\text{Total number of respondents}} = \frac{1249}{2082} $$

**Numerical Calculation:**
$$ \frac{1249}{2082} \approx 0.599 \text{ or } 59.9\% $$

**Answer:**
The probability is approximately **59.9%**.

---

### **B. Probability that a respondent in the $$ 18-34 $$ age group owned a home**

**Calculation:**
$$ \text{Probability} = \frac{\text{Number of "Yes" responses in 18-34}}{\text{Total respondents in 18-34 age group}} = \frac{117}{450} $$

**Numerical Calculation:**
$$ \frac{117}{450} = 0.26 \text{ or } 26.0\% $$

**Answer:**
The probability is **26.0%**.

---

### **C. Probability that a respondent to the poll did not own a home**

**Calculation:**
$$ \text{Probability} = 1 - \text{Probability of owning a home} = 1 - \frac{1249}{2082} $$
$$ = \frac{2082 - 1249}{2082} = \frac{833}{2082} $$

**Numerical Calculation:**
$$ \frac{833}{2082} \approx 0.3995 \text{ or } 40.0\% $$

**Answer:**
The probability is approximately **40.0%**.

---

### **D. Probability that a respondent in the $$ 18-34 $$ age group did not own a home**

**Calculation:**
$$ \text{Probability} = 1 - \text{Probability of owning a home in 18-34} = 1 - \frac{117}{450} $$
$$ = \frac{450 - 117}{450} = \frac{333}{450} $$

**Numerical Calculation:**
$$ \frac{333}{450} = 0.74 \text{ or } 74.0\% $$

**Answer:**
The probability is **74.0%**.

---

### **Summary of Probabilities:**
- **A.** 59.9%
- **B.** 26.0%
- **C.** 40.0%
- **D.** 74.0%
- **A.** 59.9% - **B.** 26.0% - **C.** 40.0% - **D.** 74.0%

Upstudy AI Solution

Answer

Solution

Given Data:

A. Probability that a respondent to the poll owned a home

B. Probability that a respondent in the age group owned a home

C. Probability that a respondent to the poll did not own a home

D. Probability that a respondent in the age group did not own a home

Summary of Probabilities:

Bonus Knowledge

Related Questions

Latest Probability Questions