https://file.aiquickdraw.com/mathbot/file/1729388775242xrk8t10r.jpg

Let's break down the problem step by step to fill in the table and answer the questions based on conditional probability.

### Step 1: Understanding the table

The table shows the responses of 1,010 married adults on "Who is better at getting deals?" with three options: 
1. "I am" (meaning the respondent thinks they are better),
2. "My spouse" (meaning the respondent thinks their spouse is better),
3. "We are equal" (meaning both are equally good).

The data for husbands and wives is given separately:
- **Husbands**: 278 said "I am," 127 said "My spouse," and 102 said "We are equal."
- **Wives**: 290 said "I am," 111 said "My spouse," and 102 said "We are equal."

### Step 2: Fill in the joint probability table (a)
You can now fill in the table with the counts and calculate the total for each category.

| Respondent | I am | My spouse | We are equal | Total |
|------------|------|-----------|--------------|-------|
| Husband    | 278  | 127       | 102          | 507   |
| Wife       | 290  | 111       | 102          | 503   |
| **Total**  | 568  | 238       | 204          | 1010  |

Now let's proceed to the questions.

### Step 3: Marginal probabilities (b)
- Probability of "I am" = $ \frac{568}{1010} \approx 0.5624 $
- Probability of "My spouse" = $ \frac{238}{1010} \approx 0.2356 $
- Probability of "We are equal" = $ \frac{204}{1010} \approx 0.2010 $

### Step 4: Conditional probabilities (c) through (f)

- **c. Given that the respondent is a husband, the probability that he feels he is better at getting deals than his wife** = $ \frac{278}{507} \approx 0.5487 $
- **d. Given that the respondent is a wife, the probability that she feels she is better at getting deals than her husband** = $ \frac{290}{503} \approx 0.5763 $
- **e. Given a response "my spouse" is better at getting deals, the probability that the response came from a husband** = $ \frac{127}{238} \approx 0.5336 $
- **f. Given a response "we are equal," the probability that the response came from a husband** = $ \frac{102}{204} = 0.5000 $

Let me know if you'd like to dive deeper into any specific part or need further clarification.

---

Here are five follow-up questions:
1. How do we calculate joint probabilities using the data provided?
2. Can you explain the concept of marginal probability in more detail?
3. How does conditional probability differ from joint probability?
4. Why is the probability of "We are equal" the same for both husbands and wives?
5. How would the table change if the total number of respondents were different?

**Tip**: In conditional probability, always make sure to carefully identify the "given" condition, as it changes the sample space.

To better understand how husbands and wives feel about their finances, Money Magazine conducted a national poll of 1,010 married adults aged 25 and older with household incomes of $50,000 or more. The question asked was 'Who is better at getting deals?'

This problem involves conditional probability and marginal probability. It explores how husbands and wives perceive their ability to get deals, based on a national poll of 1,010 married adults. It involves calculating joint and conditional probabilities using provided data.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation