Four hundred consumers are surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24	25–34	35–55	55 and over	Total
Liked Crunchicles	14	17	22	48	101
Disliked Crunchicles	26	43	14	70	153
No Preference	7	10	8	121	146
Total	47	70	44	239	400

One consumer from the survey is selected at random. Leave all answers in a reduced fraction.
What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?

What is the probability that the selected consumer dislikes Crunchicles?

What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?

If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?

Let's break down each question one by one using the data provided in the table. The total number of consumers surveyed is 400, and we have different categories based on age groups and preferences.

#### 1. **What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles?**

We use conditional probability:
\[
P(\text{18-24} \mid \text{Dislikes Crunchicles}) = \frac{P(\text{18-24 and Dislikes Crunchicles})}{P(\text{Dislikes Crunchicles})}
\]

From the table, the number of consumers who are 18-24 and dislike Crunchicles is 26, and the total number of consumers who dislike Crunchicles is 153. Therefore:

\[
P(\text{18-24} \mid \text{Dislikes Crunchicles}) = \frac{26}{153}
\]

#### 2. **What is the probability that the selected consumer dislikes Crunchicles?**

This is simply the ratio of consumers who dislike Crunchicles to the total number of consumers surveyed:

\[
P(\text{Dislikes Crunchicles}) = \frac{153}{400}
\]

#### 3. **What is the probability that the selected consumer is 35–55 years old or likes Crunchicles?**

This question asks for the probability that the consumer belongs to either of two mutually inclusive events (being 35-55 years old or liking Crunchicles). We use the formula for the union of two events:

\[
P(\text{35-55 or Likes Crunchicles}) = P(\text{35-55}) + P(\text{Likes Crunchicles}) - P(\text{35-55 and Likes Crunchicles})
\]

From the table:
- The number of 35-55-year-olds is 44.
- The number of people who like Crunchicles is 101.
- The number of people who are 35-55 and like Crunchicles is 22.

Now calculate:

\[
P(\text{35-55 or Likes Crunchicles}) = \frac{44}{400} + \frac{101}{400} - \frac{22}{400} = \frac{123}{400}
\]

#### 4. **If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?**

Since age group 55 and over contains consumers who are 70 years old, we need to calculate the conditional probability:

\[
P(\text{Likes Crunchicles} \mid \text{55 and over}) = \frac{P(\text{Likes Crunchicles and 55 and over})}{P(\text{55 and over})}
\]

From the table:
- The number of consumers 55 and over who like Crunchicles is 48.
- The total number of consumers 55 and over is 239.

Thus:

\[
P(\text{Likes Crunchicles} \mid \text{55 and over}) = \frac{48}{239}
\]

---

### Recap of Answers:
1. \( \frac{26}{153} \)
2. \( \frac{153}{400} \)
3. \( \frac{123}{400} \)
4. \( \frac{48}{239} \)

Would you like more details on any of these calculations?

### Related Questions:
1. What is the probability that the consumer is 25-34, given they like Crunchicles?
2. What is the probability that a randomly selected consumer is 18–24 years of age?
3. What is the probability that a consumer has no preference?
4. What is the probability that a consumer dislikes Crunchicles and is over 55 years of age?
5. What is the probability that the consumer is 35-55 years old, given that they have no preference?

### Tip:
When calculating probabilities involving "or" (union) of events, remember to subtract the overlap to avoid double-counting!

Four hundred consumers are surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table. 18–24: 14 liked, 26 disliked, 7 no preference. 25–34: 17 liked, 43 disliked, 10 no preference. 35–55: 22 liked, 14 disliked, 8 no preference. 55 and over: 48 liked, 70 disliked, 121 no preference. What is the probability that the consumer is 18–24 years of age, given that he/she dislikes Crunchicles? What is the probability that the selected consumer dislikes Crunchicles? What is the probability that the selected consumer is 35–55 years old or likes Crunchicles? If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?

Explore probability concepts using a consumer survey of 400 people about a new snack food, Crunchicles. Learn to calculate conditional probabilities, overall probabilities, and the union of events using real survey data. Suitable for Grades 9-12.

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