# Expected number of winners in this basket-like betting game?

Given $n$ players and $m$ baskets. Each player has random distinct label from the set $\{1, ..., n\}$. Each player $i$ selects a set of baskets $B(i)$ uniformly randomly with probability $p$. Then, each player $i$ puts a paper with his/her label in all the baskets in $B(i)$. A player $i$ win a basket $j \in B(i)$ if the paper he puts in $j$ is the smallest.

What is the expected number of winners ?

Find the probability player $i$ wins a particular basket.
Use this to find the probability player $i$ wins at least one basket.