Question
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?
A Venn diagram shows the results of a survey of 100 people regarding their favorite way to eat ice cream. Three circles intersect and are labeled to show the data.
(7 points)
Responses
39100
39 over 100
12100
12 over 100
15100
15 over 100
85100
A Venn diagram shows the results of a survey of 100 people regarding their favorite way to eat ice cream. Three circles intersect and are labeled to show the data.
(7 points)
Responses
39100
39 over 100
12100
12 over 100
15100
15 over 100
85100
Answers
GPT-4o mini
To find the probability that a person prefers sprinkles or prefers chocolate on their ice cream based on the Venn diagram you described, we need to understand how many people prefer sprinkles, chocolate, or both, and then calculate the probability from that group.
From the information provided, you appear to have given several fractions that may correspond to the number of people who expressed certain preferences:
- 39 people prefer sprinkles
- 12 people prefer chocolate
- 15 people prefer both sprinkles and chocolate
- 85 people prefer neither sprinkles nor chocolate (implying they might prefer another option or none at all)
To compute the total number of people who prefer sprinkles or chocolate (including those who may like both), we use the formula for the union of two sets:
\[ P(S \cup C) = P(S) + P(C) - P(S \cap C) \]
Where:
- \( P(S) \) is the number of people who prefer sprinkles.
- \( P(C) \) is the number of people who prefer chocolate.
- \( P(S \cap C) \) is the number of people who prefer both sprinkles and chocolate.
Given your data:
- \( P(S) = 39 \)
- \( P(C) = 12 \)
- \( P(S \cap C) = 15 \)
Substituting these numbers into the equation gives:
\[ P(S \cup C) = 39 + 12 - 15 = 36 \]
Now, the probability that a randomly selected person prefers sprinkles or chocolate is given by:
\[
P(\text{Sprinkles or Chocolate}) = \frac{P(S \cup C)}{100} = \frac{36}{100} = 0.36
\]
Thus, the probability that a randomly selected person prefers sprinkles or chocolate on their ice cream is **0.36** or **36%**.
In your survey:
- Probability \( = \frac{36}{100} \) or in decimal form, **0.36**.
From the information provided, you appear to have given several fractions that may correspond to the number of people who expressed certain preferences:
- 39 people prefer sprinkles
- 12 people prefer chocolate
- 15 people prefer both sprinkles and chocolate
- 85 people prefer neither sprinkles nor chocolate (implying they might prefer another option or none at all)
To compute the total number of people who prefer sprinkles or chocolate (including those who may like both), we use the formula for the union of two sets:
\[ P(S \cup C) = P(S) + P(C) - P(S \cap C) \]
Where:
- \( P(S) \) is the number of people who prefer sprinkles.
- \( P(C) \) is the number of people who prefer chocolate.
- \( P(S \cap C) \) is the number of people who prefer both sprinkles and chocolate.
Given your data:
- \( P(S) = 39 \)
- \( P(C) = 12 \)
- \( P(S \cap C) = 15 \)
Substituting these numbers into the equation gives:
\[ P(S \cup C) = 39 + 12 - 15 = 36 \]
Now, the probability that a randomly selected person prefers sprinkles or chocolate is given by:
\[
P(\text{Sprinkles or Chocolate}) = \frac{P(S \cup C)}{100} = \frac{36}{100} = 0.36
\]
Thus, the probability that a randomly selected person prefers sprinkles or chocolate on their ice cream is **0.36** or **36%**.
In your survey:
- Probability \( = \frac{36}{100} \) or in decimal form, **0.36**.