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)

1 answer

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 they like 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:

  • The number of people who like both apples and comedy is 12.
  • The total number of people who like comedy is 22.

Thus, we can calculate:

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

To reduce this fraction, we find the greatest common divisor (GCD) of 12 and 22, which is 2. Dividing both the numerator and the denominator by 2 gives:

\[ P(A | B) = \frac{12 \div 2}{22 \div 2} = \frac{6}{11} \]

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

\(\frac{6}{11}\)