Two customers Shyam and Ekta 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 the same day?

Let S be the event that Shyam visits the shop and E be the event that Ekta visits the shop.
The week consists of 5 days (Tuesday to Saturday).
Each customer is equally likely to visit the shop on any of the 5 days.
The probability that Shyam visits the shop on a particular day is 1/5. Similarly, the probability that Ekta visits the shop on a particular day is 1/5.
We want to find the probability that both Shyam and Ekta visit the shop on the same day. This can happen in 5 ways:

1. Both visit on Tuesday
2. Both visit on Wednesday
3. Both visit on Thursday
4. Both visit on Friday
5. Both visit on Saturday

The probability that both visit on Tuesday is (1/5) * (1/5) = 1/25
The probability that both visit on Wednesday is (1/5) * (1/5) = 1/25
The probability that both visit on Thursday is (1/5) * (1/5) = 1/25
The probability that both visit on Friday is (1/5) * (1/5) = 1/25
The probability that both visit on Saturday is (1/5) * (1/5) = 1/25

Since these events are mutually exclusive, the probability that both visit on the same day is the sum of the probabilities of these events:

P(both visit on the same day) = P(Tuesday) + P(Wednesday) + P(Thursday) + P(Friday) + P(Saturday)
= 1/25 + 1/25 + 1/25 + 1/25 + 1/25
= 5/25
= 1/5

Therefore, the probability that both Shyam and Ekta will visit the shop on the same day is 1/5.