The first problem is much simpler framed around Bernoulli sequences, each concluding when one gets another distinct toy. Then, it's just the expectation of the

The first problem is much simpler framed around Bernoulli sequences, each concluding when one gets another distinct toy. Then, it's just the expectation of the sum of four geometric random variables If you have zero toys, the probability of getting a new distinct toy is 1. With 1, it's 3/4. With 2, it's 1/2. With 3, it's 1/4. Then, expected number of meals to get all the toys is 1/1 + 1/(3/4) + 1/(1/2) + 1/(1/4)