Question

Recall from the lesson that this Venn diagram represents 100 people’s responses to three different statements about their favorite ways to eat ice cream. Based on the diagram, what is the probability that a person prefers sprinkles or prefers chocolate on their ice cream? Express your answer as a fraction. You do not need to reduce.

Answer 1

To find the probability that a person prefers sprinkles or prefers chocolate on their ice cream based on the provided Venn diagram, we need to determine the total number of people who prefer sprinkles, chocolate, or both.

Suppose from the Venn diagram:
- Let \( S \) be the number of people who prefer sprinkles.
- Let \( C \) be the number of people who prefer chocolate.
- Let \( S \cap C \) be the number of people who prefer both sprinkles and chocolate.

The number of people who prefer sprinkles or chocolate (or both) can be calculated using the formula for the union of two sets:
\[
|S \cup C| = |S| + |C| - |S \cap C|
\]

Once we have \( |S \cup C| \), the probability that a person prefers sprinkles or chocolate can be determined by dividing the number of people in that union by the total number of surveyed people (100 in this case).

So the probability \( P(S \cup C) \) is given by:
\[
P(S \cup C) = \frac{|S \cup C|}{100}
\]

Without specific values from the Venn diagram, we can’t calculate an exact fraction. However, if you provide the counts for preferences as represented in the diagram, I can help you find the exact probability.