To determine the probability that a person prefers sprinkles or chocolate on their ice cream based on the Venn diagram, we need to calculate the total number of people who prefer either sprinkles, chocolate, or both.
Let:
- \( S \) = number of people who prefer sprinkles
- \( C \) = number of people who prefer chocolate
- \( S \cap C \) = number of people who prefer both sprinkles and chocolate
The probability we are looking for can be expressed using the formula for the union of two sets:
\[ P(S \cup C) = P(S) + P(C) - P(S \cap C) \]
Using the data from the Venn diagram:
- Count the total number of people who prefer sprinkles (including those who also like chocolate).
- Count the total number of people who prefer chocolate (including those who also like sprinkles).
- Count how many like both sprinkles and chocolate.
Assuming we found:
- \( n(S) \) = total people who prefer sprinkles
- \( n(C) \) = total people who prefer chocolate
- \( n(S \cap C) \) = total people who prefer both
With these counts, we can find the total number of people who prefer either sprinkles or chocolate and calculate the probability as follows:
\[ n(S \cup C) = n(S) + n(C) - n(S \cap C) \]
Finally, since the total number of respondents is 100, the probability is:
\[ P(S \cup C) = \frac{n(S \cup C)}{100} \]
Once you have the values from the Venn diagram, substitute them into the calculations above to get the desired probability in fraction form.
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