Expected Trials Two Coupons

Problem

If each trial independently yields coupon A with probability p1, coupon B with probability p2, or neither, the expected number of trials until both have appeared is 1/p1 + 1/p2 - 1/(p1 + p2).

Given p1 and p2 with p1 + p2 <= 1, return the expectation.

Hint

Inclusion-exclusion over the two waiting times.

Test cases

case 1

in: [0.1,0.2]

expected: 11.666666666666668

case 2

in: [0.5,0.5]

expected: 3

case 3

in: [0.25,0.25]

expected: 6

Starter codePython

def expected_trials_two_coupons(p1, p2):
    # Your code here
    pass

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