The management of an indoor shopping mall randomly selects one store from each differently colored section, choosing stores 2, 8, 28, and 40. They survey all shoppers in these selected stores to gather opinions on store layouts. The probability of this specific selection depends on the total number of stores in each colored section.
The scenario you described involves the management of an indoor shopping mall conducting a survey about the layout of the stores in the mall. Here's a step-by-step explanation of what's happening:
1. The mall is divided into differently colored sections: This means that the mall is organized into distinct areas or zones, each with a different color designation. These sections likely help shoppers navigate through the mall.
2. Randomly selecting stores: The management wants to survey shoppers' opinions on store layouts, so they need to select a representative sample of stores to gather data from. To ensure the sample is random, they use a random selection method.
3. Store selection: The management has chosen four specific stores for the survey, and these stores are numbered 2, 8, 28, and 40. These store numbers have been randomly selected from the mall's stores.
4. Surveying all shoppers in each selected store: Once the stores are selected, the management plans to survey all of the shoppers present in each of the four chosen stores. This means they will approach and gather feedback from every shopper in these stores during the survey.
Now, let's calculate some probabilities:
a. Probability of selecting any specific store:
Since the management randomly selects one store from each colored section, the probability of selecting any specific store within a section is 1 divided by the total number of stores in that section. If we assume that each colored section has the same number of stores, then the probability of selecting any specific store within a section is 1 divided by the total number of stores in a section.
b. Probability of selecting the four specific stores (2, 8, 28, and 40):
To calculate the probability of this specific outcome, we need to multiply the individual probabilities of selecting each store. Since each store is chosen independently, the probability of selecting all four stores is the product of the probabilities for each store.
Let's assume there are 'N' stores in each colored section, and 'C' colored sections in the mall.
- Probability of selecting store 2 = 1/N
- Probability of selecting store 8 = 1/N
- Probability of selecting store 28 = 1/N
- Probability of selecting store 40 = 1/N
Probability of selecting all four stores = (1/N) × (1/N) × (1/N) × (1/N) =
So, the probability of this specific outcome depends on the total number of stores in each colored section (N) and the number of colored sections in the mall (C). If you have these values, you can calculate the exact probability using the formula above.