Use the table to answer the question.

Question

Drink Preference
Food Preference Soda Preference Sweet Tea Preference Total
Soup 11 29 40
Salad 38 32 70
Total 49 61 110
Given that someone prefers sweet tea, what is the probability that they also prefer salad? Leave your answer as a reduced fraction.

(1 point)

Answer 1

To find the probability that someone prefers salad given that they prefer sweet tea, we can use the formula for conditional probability:

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

Where:

• \( A \) is the event of preferring salad.
• \( B \) is the event of preferring sweet tea.

From the table:

• The total number of people who prefer sweet tea is 61.
• The number of people who prefer both salad and sweet tea is 32.

Now we can substitute these values into the conditional probability formula:

\[ P(\text{Salad} | \text{Sweet Tea}) = \frac{P(\text{Salad} \cap \text{Sweet Tea})}{P(\text{Sweet Tea})} = \frac{32}{61} \]

Thus, the probability that someone prefers salad given that they prefer sweet tea is:

\[ \frac{32}{61} \]

This fraction is already in its reduced form. Therefore, the final answer is:

\[ \boxed{\frac{32}{61}} \]