Use the table to answer the 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 will use the formula for conditional probability.

The formula is given by:

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

Where:

• \(P(A | B)\) is the probability that event A occurs given that event B has occurred.
• \(P(A \cap B)\) is the probability that both events A and B occur.
• \(P(B)\) is the probability that event B occurs.

In this case:

• Let event A be the preference for salad.
• Let event B be the preference for sweet tea.

From the table:

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

We can calculate \(P(A \cap B)\) and \(P(B)\):

1. \(P(A \cap B) = \text{Number of people who prefer both salad and sweet tea} = 32\)
2. \(P(B) = \text{Total number of people who prefer sweet tea} = 61\)

Now, plug these values into the conditional probability formula:

\[ P(A | B) = \frac{P(A \cap B)}{P(B)} = \frac{32}{61} \]

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

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