To determine the probability that a person prefers sprinkles or chocolate on their ice cream based on the Venn diagram, you'll want to find the total number of people who prefer either sprinkles, chocolate, or both.
Let’s represent the counts 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 probability that a person prefers sprinkles or chocolate can be calculated using the formula for the union of two sets: \[ P(S \cup C) = P(S) + P(C) - P(S \cap C) \] This gives the total number of unique individuals who prefer either sprinkles or chocolate.
Assuming we have the values from the Venn diagram:
- Let’s denote \( n(S) \) as the total number of people who prefer sprinkles.
- Let’s denote \( n(C) \) as the total number of people who prefer chocolate.
- Let’s denote \( n(S \cap C) \) as the total number of people who prefer both.
Let's say:
- \( n(S) = A \)
- \( n(C) = B \)
- \( n(S \cap C) = C \)
Thus, the total number of people who prefer either sprinkles or chocolate is: \[ n(S \cup C) = A + B - C \]
To find the probability, divide this total by the number of surveyed people (100): \[ P(S \cup C) = \frac{A + B - C}{100} \]
If you have the specific values from the Venn diagram, substitute them into the equation above.
Let's say for the sake of example:
- \( n(S) = 30 \)
- \( n(C) = 40 \)
- \( n(S \cap C) = 10 \)
Then:
- \( n(S \cup C) = 30 + 40 - 10 = 60 \)
The probability that a person prefers sprinkles or chocolate is then: \[ P(S \cup C) = \frac{60}{100} \]
Thus, you would express your final answer as: \[ \frac{60}{100} \]
Make sure to use the actual numbers from the Venn diagram to get your final answer.
11 answers