Question

This two-way table shows the preference of ice cream for different age groups.

ice cream table

Given that someone picked chocolate, what is the probability that they are an adult?

Question 5 options:

0.374


0.112


0.372


0.514

Answer 1

To find the probability that someone is an adult given that they picked chocolate, we can use Bayes' theorem or the concept of conditional probability. However, we need the data from the two-way table showing the counts of preferences of ice cream among different age groups.

Let's denote:
- \(A\): the event that the person is an adult.
- \(C\): the event that the person picked chocolate.

We want to find \(P(A | C)\), which is the probability of being an adult given that the person chose chocolate.

Using the formula for conditional probability:

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

Where:
- \(P(A \cap C)\) is the probability that the person is both an adult and picked chocolate.
- \(P(C)\) is the probability that the person picked chocolate.

Now, for the calculations:

1. Count the number of adults who picked chocolate from the table. Let's say this number is \(N(A \cap C)\).
2. Count the total number of people who picked chocolate. Let's say this number is \(N(C)\).
3. The total number of responses in the survey gives us the overall \(N\).

Now, we can calculate:

\[
P(A | C) = \frac{N(A \cap C) / N}{N(C) / N} = \frac{N(A \cap C)}{N(C)}
\]

Since you have provided options but no table data, I can't provide a numerical answer.

Could you please provide the counts from the two-way table for adults and kids for chocolate flavor? This will allow us to perform the calculations needed to find the probability.