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?

In this context:

1. 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.

2. 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:
\[
P(\text{Pharmacy} \cap \text{Floral} \cap \text{Deli}) = 0.10
\]

Therefore, the probability of selecting a store that **does not have all three departments** is the complement of this probability:
\[
P(\text{not all three departments}) = 1 - P(\text{all three departments}) = 1 - 0.10 = 0.90
\]

### Answer Summary:
1. The name for the event of selecting a store with a pharmacy, floral shop, and deli is the **intersection of three events**.
2. 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:

1. What is the probability of selecting a store that has at least one of these departments?
2. How would you calculate the probability of a store having only two of the three departments?
3. Can you verify the information given using a Venn diagram or inclusion-exclusion principle?
4. How do you interpret joint probabilities in survey data?
5. 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.

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 pharmacy 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 pharmacy, a floral shop, and a deli'? What is the probability of selecting a store that does not have all three departments?

Explore the probability concepts and set theory involved in determining the likelihood of selecting a store in Eastern Canada with all three departments: pharmacy, floral shop, and deli. This problem uses the inclusion-exclusion principle and the complementary rule to find probabilities, ideal for high school students.

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