Polya Urn Expected Red

Problem

A Polya urn starts with r red and b blue balls. Each draw removes a ball and returns it with one extra ball of the same color. Return the expected number of red balls after n draws:

E[R_n] = r + n * r / (r + b).

Return 0.0 when the urn is empty or n < 0.

Hint

The probability the next drawn ball is red stays r / (r + b).

Test cases

case 1

in: [1,1,2]

expected: 2

case 2

in: [2,3,5]

expected: 4

case 3

in: [4,6,0]

expected: 4

case 4

in: [0,5,3]

expected: 0

Starter codePython

def polya_urn_expected_red(r, b, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor