Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

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 ?

share|improve this question
    
Welcome to the site, @Ajed. Note that homework problems get special treatment here--you get hints to help you work though the problem for yourself, but not answers. These topics (& more) are discussed in our FAQ, which you may want to read. –  gung Nov 1 '12 at 3:48
    
No No it is not a homework .. believe me. It just a question that came to my mind. –  AJed Nov 1 '12 at 15:25
    
Sorry about that, @Ajed, it looked like HW to me. If you would prefer hints to help you think through the problem, leave it as is. If you just want someone to give you a complete solution, edit your question to remove the HW tag. –  gung Nov 1 '12 at 15:33
    
no problem ! :) –  AJed Nov 1 '12 at 18:14

1 Answer 1

up vote 0 down vote accepted

Find the probability player $i$ wins a particular basket.

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

Add these probabilities.

share|improve this answer
    
thanks for the hint –  AJed Nov 1 '12 at 20:40

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.