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?

Submit

Let's solve each part of this question step by step using probability formulas.

### 1. **Probability that the consumer is 18–24 years of age, given that they dislike Crunchicles:**

This is a conditional probability problem. The formula for conditional probability is:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Where:
- \( A \) is the event "consumer is 18–24 years of age."
- \( B \) is the event "consumer dislikes Crunchicles."

From the table, the number of consumers who are both 18–24 years of age **and** dislike Crunchicles is 26. The total number of consumers who dislike Crunchicles is 153.

So:

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

### 2. **Probability that the selected consumer dislikes Crunchicles:**

This is simply the proportion of consumers who dislike Crunchicles out of the total surveyed population. From the table, the total number of consumers who dislike Crunchicles is 153, and the total number of consumers surveyed is 400.

So:

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

### 3. **Probability that the selected consumer is 35–55 years old or likes Crunchicles:**

This is the probability of the union of two events: being 35–55 years old **or** liking Crunchicles. The formula for the probability of the union of two events is:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

Where:
- \( A \) is the event "consumer is 35–55 years old."
- \( B \) is the event "consumer likes Crunchicles."

From the table:
- The number of consumers who are 35–55 years old is 44.
- The number of consumers who like Crunchicles is 101.
- The number of consumers who are both 35–55 years old **and** like Crunchicles is 22.

Now, let's calculate:

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

### 4. **Probability that a 70-year-old consumer likes Crunchicles:**

Since we're specifically given the consumer is 70 years old, this is another conditional probability problem.

Assume that a consumer who is 70 years old falls under the age group "55 and over."

The total number of consumers in the age group "55 and over" is 239, and the number of consumers in this group who like Crunch

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

Calculate various probabilities based on a survey of 400 consumers about their preference for a new snack brand, Crunchicles. Learn to find conditional probability, probability of union of events, and specific age-based probabilities with a detailed solution suitable for Grades 9-12 students.

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