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A survey of grocery stores in the Southeast revealed 40
Chapter 5, Problem 21E(choose chapter or problem)
Problem 21E
A survey of grocery stores in the Southeast revealed 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli. Suppose 10 percent of the stores have all three departments, 30 percent have both a pharmacy and a deli, 25 percent have both a floral shop and deli, and 20 percent have both a pharmacy and floral shop.
a. What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop?
b. What is the probability of selecting a store at random and finding it has both a pharmacy and a deli?
c. Are the events “select a store with a deli” and “select a store with a pharmacy” mutually exclusive?
d. What is the name given to the event of “selecting a store with a pharmacy, a floral shop, and a deli?”
e. What is the probability of selecting a store that does not have all three departments?
Questions & Answers
QUESTION:
Problem 21E
A survey of grocery stores in the Southeast revealed 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli. Suppose 10 percent of the stores have all three departments, 30 percent have both a pharmacy and a deli, 25 percent have both a floral shop and deli, and 20 percent have both a pharmacy and floral shop.
a. What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop?
b. What is the probability of selecting a store at random and finding it has both a pharmacy and a deli?
c. Are the events “select a store with a deli” and “select a store with a pharmacy” mutually exclusive?
d. What is the name given to the event of “selecting a store with a pharmacy, a floral shop, and a deli?”
e. What is the probability of selecting a store that does not have all three departments?
ANSWER:
Solution:
Step 1 of 5:
A survey of grocery stores in the Southeast says that 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli.
Here 10 per cent of the stores have all three departments, 30 percent have both pharmacy and a deli, 25 percent have both a floral shop and deli, and 20 percent have both a pharmacy and floral shop.
- We have to find the probability of selecting a store at random and finding it has both pharmacy and a floral shop.
- We have to find the probability of selecting a store at random and finding it has both a pharmacy and a deli.
- We have to find whether the events “select a store with a deli” and “ selecting a store with a pharmacy” are mutually exclusive.
- We have to find the event of “selecting a store with a pharmacy, a floral shop, and a deli.
- We have to find the probability of selecting a store that does not have all three departments.