Let's solve the questions based on the table provided in the image. I'll refer to the numbers directly from the image and work through each problem.

1. Probability that the consumer is 18-24 years old, given that he/she dislikes Crunchicles?

This is a conditional probability problem. We are given that the consumer dislikes Crunchicles (which is 180 people total), and we need to find the probability that this person is in the 18-24 age group.

The formula for conditional probability is:

$P(\text{A | B}) = \frac{P(\text{A and B})}{P(\text{B})}$

Here, A = "18-24 years old" and B = "Dislikes Crunchicles".

• Number of people who are 18-24 and dislike Crunchicles: 14
• Total number of people who dislike Crunchicles: 180

Thus, the probability is:

$P(\text{18-24 | Dislikes Crunchicles}) = \frac{14}{180} = \frac{7}{90}$

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

To find this probability, we need to calculate the ratio of consumers who dislike Crunchicles to the total number of consumers.

• Number of people who dislike Crunchicles: 180
• Total number of people surveyed: 500

Thus, the probability is:

$P(\text{Dislikes Crunchicles}) = \frac{180}{500} = \frac{9}{25}$

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

This requires finding the probability of the union of two events:

• A = "35-55 years old"
• B = "Likes Crunchicles".

The formula for the probability of $A$ or $B$ is:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

• Number of people aged 35-55: 73
• Number of people who like Crunchicles: 150
• Number of people who are 35-55 and like Crunchicles: 20

Thus,

$P(\text{35-55 years old or Likes Crunchicles}) = \frac{73}{500} + \frac{150}{500} - \frac{20}{500} = \frac{73 + 150 - 20}{500} = \frac{203}{500}$

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

Assuming people aged 70 fall into the "55 and over" category:

• Total number of people aged 55 and over: 239
• Number of people aged 55 and over who like Crunchicles: 35

Thus, the conditional probability is:

$P(\text{Likes Crunchicles | 55 and over}) = \frac{35}{239}$

Let me know if you'd like further explanation on any of the steps or more details! Here are 5 related questions for further practice:

1. What is the probability that the selected consumer is 25-34 years old, given that he/she likes Crunchicles?
2. What is the probability that the selected consumer is 55 and over, given that they have no preference for Crunchicles?
3. What is the probability that a consumer aged 18-24 either dislikes Crunchicles or has no preference?
4. If a consumer is randomly selected, what is the probability that they have no preference for Crunchicles?
5. What is the probability that a consumer aged 35-55 dislikes Crunchicles?

Tip: Always carefully identify the total number related to the condition when calculating conditional probabilities.