Day 4: Geometric Distribution II

Objective
In this challenge, we go further with geometric distributions. We recommend reviewing the Geometric Distribution tutorial before attempting this challenge.

Task
The probability that a machine produces a defective product is . What is the probability that the defect is found during the first inspections?

Input Format

The first line contains the respective space-separated numerator and denominator for the probability of a defect, and the second line contains the inspection we want the probability of the first defect being discovered by:

1 3
5

If you do not wish to read this information from stdin, you can hard-code it into your program.

Output Format

Print a single line denoting the answer, rounded to a scale of decimal places (i.e., format).