Question

Suppose that 10% of apples in a supermarket are rotten. The manager checks the stock of apples, by inspecting them one at a time. What is the probability that the 7th apple he inspects is the rotten one he finds? What distribution does the variable “number of inspected apples until the first rotten one” follow?

Answer 1

This is an example of gemetric distribuiton or a special case of negative binomial distribution.

g(x,P) = P x Q-1 g(7,0.1) = 0.1 x 0.97-1 = 0.05314

The distribution the variable “number of inspected apples until the first rotten one” follow a binomial distribution