Math Problem Statement
A survey of grocery stores in Eastern Canada revealed that 40% had a pharmacy, 50% has a floral shop, and 70% had a deli. Suppose 10% of the stores have all three departments, 30% have both a pharmany and a deli, 25% have both a floral shop and deli, and 20% have both a pharmacy and a floral shop.What is the name given to the event of "selecting a store with a pharmany, a floral shop, and a deli"?What is the probability of selecting a store that does not have all three departments?
Solution
In this context:
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The event of "selecting a store with a pharmacy, a floral shop, and a deli" is called the intersection of three events or joint occurrence of these three departments.
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To determine the probability of selecting a store that does not have all three departments, we can use the given probability information directly.
Since 10% of the stores have all three departments, the probability of selecting a store with all three departments is:
Therefore, the probability of selecting a store that does not have all three departments is the complement of this probability:
Answer Summary:
- The name for the event of selecting a store with a pharmacy, floral shop, and deli is the intersection of three events.
- The probability of selecting a store that does not have all three departments is 0.90 (or 90%).
Would you like more details on the solution or clarification? Here are some related questions to expand understanding:
- What is the probability of selecting a store that has at least one of these departments?
- How would you calculate the probability of a store having only two of the three departments?
- Can you verify the information given using a Venn diagram or inclusion-exclusion principle?
- How do you interpret joint probabilities in survey data?
- What would change in calculations if the survey included more departments?
Tip: For multi-category probability problems, drawing a Venn diagram helps visualize overlaps and interactions.
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Math Problem Analysis
Mathematical Concepts
Probability
Set Theory
Complementary Events
Formulas
P(A ∩ B ∩ C) = Probability of intersection of three events
P(not A ∩ B ∩ C) = 1 - P(A ∩ B ∩ C)
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 10-12
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