As a part of a customer loyalty program, a restaurant’s computer chooses orders at random to receive a free appetizer. Each order has a 1 in 18chance of receiving a free appetizer. (Each order is limited to one free appetizer.) Let X be the number of orders the restaurant fills in a day until they give away the first appetizer. Assume that each order getting the appetizer is independent.

Find the probability that the restaurant first gives away an appetizer on the 6^{\text{th}}6th6, start superscript, start text, t, h, end text, end superscript order of the day.
You may round your answer to the nearest hundredth.

Solution:

(1)