Probability

Question

You are five years old, and each time you finish a box of cereal, the manufacturer sends you a little toy.

There are four different types of toys. Each time the company sends out a toy, they pick the type of toy at random (uniformly).

On average, how many boxes of cereal (should be an integer) must you eat in order to get a complete collection, i.e. one of each type of toy?

Answer 1

Similar to coupon collector problem.

$E(No. \ of \ boxes) = \sum_{k=0}^{3}\frac{4}{4-k}$ $\approx$ 8
 

Proof : https://gateoverflow.in/?qa=blob&qa_blobid=934648949570119726