Suppose Walmart has 104 kinds of products The probability to

Suppose Walmart has 10^4 kinds of products

The probability to pick up one product is 10^-4

The probability to pick up a particular set of 10 products is about 10^-40

What is the chance this particular set of 10 products to be frequent 10^3 times in 10^9 transactions

This is a Data Mining Question but using the characteristics of probability

Solution

Total kinds = 10000

P for each = 10^-4

As trials are independent we can consider taking 10 products with p = 10^-40 as binomial with n = 10⁹

Hence Prob (successful = 10^3) = 10^9 C 10^3 (10^-40)¹⁰⁰⁰⁰ (1-10^-40)^{(10^9-10000)}