Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

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Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

| Age Group      | Liked Crunchicles | Disliked Crunchicles | No Preference | Total |
|----------------|-------------------|----------------------|---------------|-------|
| 18-24          | 1                 | 2                    | 25            | 31    |
| 25-34          | 10                | 5                    | 16            | 31    |
| 35-55          | 5                 | 2                    | 25            | 32    |
| 55 and over    | 77                | 5                    | 24            | 106   |
| **Total**      | **93**            | **17**               | **90**        | **200**|

One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.

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

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

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

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

### Detailed Explanation of the Table
The table above organizes the preferences of consumers for Crunchicles by different age groups. Here is a breakdown of the table contents:

- The rows indicate different age groups: 18-24, 25-34, 35-55, and 55 and over.
- The columns represent the preferences: whether consumers liked Crunchicles, disliked Crunchicles, or had no preference.
- Totals for each age group and each preference category are provided in the last row and last column, respectively.

For example, among those aged 18-24, 1 person liked Crunchicles, 2 disliked them, and 25 had no preference, making a total of 31 people in this age group.
Transcribed Image Text:Two hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table. | Age Group | Liked Crunchicles | Disliked Crunchicles | No Preference | Total | |----------------|-------------------|----------------------|---------------|-------| | 18-24 | 1 | 2 | 25 | 31 | | 25-34 | 10 | 5 | 16 | 31 | | 35-55 | 5 | 2 | 25 | 32 | | 55 and over | 77 | 5 | 24 | 106 | | **Total** | **93** | **17** | **90** | **200**| One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions. 1. **What is the probability that the consumer is 18-24 years of age, given that he/she dislikes Crunchicles?** 2. **What is the probability that the selected consumer dislikes Crunchicles?** 3. **What is the probability that the selected consumer is 35-55 years old or likes Crunchicles?** 4. **If the selected consumer is 70 years old, what is the probability that he/she likes Crunchicles?** ### Detailed Explanation of the Table The table above organizes the preferences of consumers for Crunchicles by different age groups. Here is a breakdown of the table contents: - The rows indicate different age groups: 18-24, 25-34, 35-55, and 55 and over. - The columns represent the preferences: whether consumers liked Crunchicles, disliked Crunchicles, or had no preference. - Totals for each age group and each preference category are provided in the last row and last column, respectively. For example, among those aged 18-24, 1 person liked Crunchicles, 2 disliked them, and 25 had no preference, making a total of 31 people in this age group.
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