What is the probability that the selected consumer is $$ 35-55 $$ years old or likes Crunchicles?
0.258

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UpStudy AI · Accepted Answer

To determine the probability that a selected consumer is either **35-55 years old** or **likes Crunchicles**, you can use the **Principle of Inclusion-Exclusion** in probability. Here's how you can approach the problem:

### **Formula:**
$$ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) $$

Where:
- $$ P(A) $$ = Probability of a consumer being **35-55 years old**
- $$ P(B) $$ = Probability of a consumer **liking Crunchicles**
- $$ P(A \text{ and } B) $$ = Probability of a consumer being **35-55 years old and liking Crunchicles**

### **Steps to Calculate:**

1. **Determine $$ P(A) $$:**
   - Find the proportion of consumers who are between 35-55 years old.

2. **Determine $$ P(B) $$:**
   - Find the proportion of consumers who like Crunchicles.

3. **Determine $$ P(A \text{ and } B) $$:**
   - Find the proportion of consumers who are both between 35-55 years old **and** like Crunchicles.

4. **Apply the Formula:**
   - Plug the values into the formula to get $$ P(A \text{ or } B) $$.

### **Example Calculation:**

Suppose you have the following data from a survey of 1,000 consumers:
- **350** are between **35-55 years old** ($$ P(A) = 0.35 $$)
- **200** like **Crunchicles** ($$ P(B) = 0.20 $$)
- **50** are both between **35-55 years old and like Crunchicles** ($$ P(A \text{ and } B) = 0.05 $$)

Using the formula:
$$ P(A \text{ or } B) = 0.35 + 0.20 - 0.05 = 0.50 $$

So, there's a **50%** probability that a randomly selected consumer is either **35-55 years old** or **likes Crunchicles**.

### **Regarding Your Answer (0.258):**

If you arrived at a probability of **0.258 (25.8%)**, please ensure that you have accurately determined the individual probabilities and their intersection. It's possible that:
- The numbers for $$ P(A) $$, $$ P(B) $$, or $$ P(A \text{ and } B) $$ might need revisiting.
- There might be overlapping categories that weren't accounted for correctly.

**If you provide the specific values for $$ P(A) $$, $$ P(B) $$, and $$ P(A \text{ and } B) $$, I can help verify the calculation more accurately.**
The probability that a selected consumer is either **35-55 years old** or **likes Crunchicles** is **0.258**.

What is the probability that the selected consumer is \( 35-55 \) years old or likes Crunchicles?\n0.258

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