Two customers A and B are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on:
consecutive days?

Answer

To find the probability that both customers A and B will visit the shop on consecutive days, we can follow these steps:

### Step 1: Identify the Days
The days of the week when the shop is open are Tuesday (T), Wednesday (W), Thursday (TH), Friday (F), and Saturday (S).

### Step 2: Determine the Sample Space
Each customer can visit the shop on any of the 5 days. Therefore, the total number of combinations of visits for customers A and B can be calculated as follows:

- For customer A, there are 5 choices (T, W, TH, F, S).
- For customer B, there are also 5 choices (T, W, TH, F, S).

Thus, the total number of outcomes in the sample space (S) is:
\[ |S| = 5 \times 5 = 25 \]

### Step 3: Identify Favorable Outcomes
Next, we need to identify the pairs of days where A and B visit the shop on consecutive days. The possible pairs of consecutive days are:

1. (T, W)
2. (W, T)
3. (W, TH)
4. (TH, W)
5. (TH, F)
6. (F, TH)
7. (F, S)
8. (S, F)

Counting these pairs gives us a total of 8 favorable outcomes (E).

### Step 4: Calculate the Probability
The probability \( P \) that both customers will visit the shop on consecutive days is given by the formula:
\[ P(E) = \frac{|E|}{|S|} \]
Substituting the values we found:
\[ P(E) = \frac{8}{25} \]

### Final Answer
The probability that both customers A and B will visit the shop on consecutive days is:
\[ \frac{8}{25} \]

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