Question

Use the table to answer the question. Fruit Preference Genre Preference Apple Preference Pear Preference Total Comedy 12 10 22 Drama 8 20 28 Total 20 30 50 Given that someone likes comedy, what is the probability that they also like apples? Leave your answer as a reduced fraction. (1 point)

Answer 1

To find the probability that someone likes apples given that they like comedy, we can use the formula for conditional probability:

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

Where:
- \( P(A | B) \) is the probability of liking apples given that the person likes comedy.
- \( P(A \cap B) \) is the number of people who like both apples and comedy.
- \( P(B) \) is the total number of people who like comedy.

From the table provided:
- The number of people who like apples and comedy (Apple Preference under Comedy) is 12.
- The total number of people who like comedy is 22.

Now we can substitute these values into the formula:

\[
P(A | B) = \frac{12}{22}
\]

Next, we reduce the fraction:

\[
\frac{12}{22} = \frac{6}{11}
\]

Thus, the probability that someone likes apples given that they like comedy is

\[
\boxed{\frac{6}{11}}.
\]