Learn / Library / Expected value

Missing sticker design

Expected valueEasy

A sticker album has $5$ equally likely designs and you already own $2$ different ones. Each new pack holds one sticker with a uniformly random design. What is the expected number of packs until you open a design you do not own yet?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Each pack is an independent trial with a fixed success probability.

Solution

Each pack shows a missing design with probability $\frac{3}{5}$ .
The number of packs up to the first success is geometric.
Its expectation is the reciprocal of $\frac{3}{5}$ , which is $\frac{5}{3}$ .

Answer: $\frac{5}{3}$

Next question Back to the library